In the Name of Allah, Most Gracious, Most Merciful.

All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.

As a matter of fact, the true Muslim always takes the advantage of the blessed occasions and days of Islam. He spares no efforts in drawing himself nearer to Allah. In doing so, he concerns himself with knowing the virtuous days and occasions in Islam so as to follow his Prophet's suit in all spheres of life.
Ibn `Abbas (may Allah be pleased with them both) said, “I never saw Allah’s Messenger (peace and blessings be upon him) so keen to fast any day and give it priority over any other than this day, the day of `Ashura', and this month, meaning Ramadan.” (Al-Bukhari) In another hadith we are told that fasting the day of `Ashura' expiates the sins of the previous year as the Prophet (peace and blessings be upon him) said,

“Fasting the day of `Ashura' (is of great merits), I hope that Allah will accept it as an expiation for (the sins committed in) the previous year” (Muslim)

Fasting the Day of `Ashura' is not to mourn the martyrdom of imam Husain (may Allah be pleased with him). We deeply respect Imam Husain’s martyrdom, we honor his glorious act of sacrifice for the sake of Islam. He gave us a great example of truth, courage and piety. But we also feel pain and grief in our hearts for his assassination at the hand of some hypocrites who took Islam as a pretext to commit their crime.

They fought and killed Allah’s Messenger’s beloved and blessed grandson and his family. This was the most heinous and shameful crime that was committed for the sake of political power. This tragic event took place in the year 61 AH or 680 CE. However, the tradition of `Ashura' fasting is very ancient and it goes back to a long time before imam Husian.

It is reported in the Sahih of Imam Al-Bukhari and other authentic collections of hadith that the Prophet (peace and blessings be upon him) and his Companions used to fast on the 10th day of Muharram while they were in Makkah (before the hijrah).

It was a day on which people of Makkah used to change the covering (kiswah) of the Ka`bah. Quraysh also used to fast on this day. (Al-Bukhari)

After the hijrah when the Prophet (peace and blessings be upon him) came to Madinah, he found that the Jews of Madinah also used to observe this day with fasting. The Prophet (peace and blessings be upon him) asked them the reason of their fasting on this day. They said, “This is a blessed day.

On this day Allah saved the Children of Israel from their enemy (in Egypt) and so Prophet Musa fasted on this day giving thanks to Allah.” The Prophet (peace and blessings be upon him) said, “We have more claim to Musa than you.” He fasted on that day and commanded Muslims to fast on this day. (Al-Bukhari)

In another report it is mentioned that Jews of Madinah used to hold a feast on this day. The Prophet (peace and blessings be upon him) told his Companions to fast instead. (Al-Bukhari)

`Ashura' fasting was obligatory (fard) in the beginning. In the second year of hijrah (624 CE) when Allah’s command came that Muslims should fast the whole month of Ramadan, the Prophet (peace and blessings be upon him) then sent someone to announce to people that fasting of `Ashura' had become voluntary (nafl). This indicates that whosoever wishes to fast, may fast and whosoever does not want to fast, there will be no blame on him/her.

Imam At-Tirmidhi mentioned that

ibn `Abbas (may Allah be pleased with them both) used to say that we should fast on two days: the 9th and 10th of Muharram to distinguish ourselves from the Jewish community. (At-Tirmidhi)

Ibn `Abbas also quoted the Prophet (peace and blessings be upon him) as saying, “If I live next year, I shall also fast on the 9th day.” (Ahmad)

There is a great reward in fasting the day of `Ashura'. There are many hadiths that mention its blessings and virtues. It is good to fast on this day, although it is not obligatory.

Allah Almighty knows best.

Excerpted, with slight modifications, from, http://pakistanlink.com

A closer look at the ahadith on Ashura
There are various ahadith to back the claim that prophet fasted on Ashura as indicated even by the OP but the following two narration summarized the gist of the remaining ahadith :

1. Narrated Ayesha:

'Ashura' was a day on which the tribe of Quraish used to fast in the pre-lslamic period of ignorance (Jahiliyyah) and the messenger of Allah also used to fast on this day. So when he migrated to Madina, he fasted on it and ordered (the Muslims) to fast on it. When the fasting of Ramadan was enjoined, it became optional for the people to fast or not to fast on the day of Ashura.”

{ Ref: Sahih Muslim, chapter: Fasting on the Day of Ashura. Book 6 Hadith2499; Book13 Hadith 143}

2. Narrated Ibn Abbas:

The holy prophet entered Madina and saw the Jews fasting on the day of Ashura. He asked them: "What is the significance of this day on which you fast?" They replied, "This is a good day, the day on which God rescued the children of Israel from their enemy. So, Moses fasted this day." He (saw) then said, "We have more claim over Moses than you." He then fasted on that day and ordered Muslims too.”

{Ref: Sahih al-Bukhari, vol. 3 Book 31, Hadith 222; Sahih Muslim- chapter: Fasting on the Day of Ashura, Book 13 Hadith 164, Book 6 Hadith2520}

In a similar version, the following is added:

"Some of the companions exclaimed 'O Messenger of God! It is a day which the Jews and the Christian hold in high esteem. Thereupon the messenger of God said: 'When the next year comes, God willing, we would observe fast on the 9th‟. But the messenger of God died before the advent of the year.

{Ref: Sahih Muslim, chapter: Fasting on the Day of Ashura, Book 13 Hadith 172 & 173; Book 6 Hadith 2528 &2529}.

CROSS EXAMINATION & SKEPTICISM

1. It is obvious from the first hadith narrated by Aisha that the practice of fasting on Ashura precede Islam; and being a Qurayshite, Muhammad (saws) used to observe and fast on that day even before being ordained as a prophet of God.

The second hadith narrated by Ibn Abbas is in sharp contradiction of the first hadith in the fact that the prophet is completely naive of the fasting on Ashura day alongside its significance. He only needs to rely on the Jewish verdict to fast and make his rulings.

* Even if the practice of Fasting on the Day of Ashura ever exist, the advent of Islam and its practices prevails over such.

The first hadith indicated, as Ramadhan was established, fasting of Ashura became of less importance where there is option to abandon.

"It is He who has sent His Apostle with guidance and the Religion of truth, that he may proclaim it over all deen (ways of life, practice, religion)..." ~Sura Saff : 9; Sura Fatih:28

2. In the second hadith, it is not conceivable that ' the messenger of God died before the advent of the (following) year (after migration to Medina) ' thereby could not fast the 9th day (tasua) of Muharram as he had reported to have legislated. Why?

* It is an established fact that the holy prophet died on the 28th Safar, 11th year of Hijrah (i.e 10 years after migration to Medina) and never the following year (2nd /3rd H) after migration which the narration portrayed. And worst still, if it is agreed that he died on the 11th year of Hijrah, it is therefore not tenable to say he did not lived to see the 9th day (tasua) of the following year since there would be about 9-10years long between his time of Migration to Medina (1Hijra) when it is alleged that he met the Jews, and his time of death (11th Hijra).

* And if it is assumed that the hadith meant the Prophet saw the Jews fasting a year before he died (i.e 9/10 H), then why does it took the prophet so long to discover the Jewish community of Madina used to fast every Ashura (10th day) of Muharram? Incidentally Prophet had a long history with the Jewish community of Madina.

Besides which Jewish clan remain in Madinah in 9th Hijrah? NONE history says. The last Jewish clan were obliterated in Khaybar in the 6th Hijrah.


WHAT THE QUR'AN SAYS?

Does it make any sense to assume the holy prophet will ever legislate or recommend a practice based on the purported verdict of the Jew?

Allah introduced him (saw) as a teacher who "...instruct them in Scripture and wisdom..." {Sura Jumu'a : 2; Al-Imran :164}

“Never will the Jews and the Christians be satisfied with thee (Muhammad) unless you follow their form of religion. Say (O Muhammad) „The guidance of God, that is the (only) Guidance.‟ Were you to follow their desires after the knowledge which has reached you, then you will neither find protector or helper against God” {Sura al-Baqarah: 120}

* Prophet's Legislation Is Only Through Inspiration And Revelation:

"(1)By the star when it goes down (2)Your companion (i.e Muhammad) is neither astray nor being mislead (3)Nor does he say (aught) of (his own) desire. (4)It is no less than inspiration sent down to him. (5)He was taught by Almighty in Power" {Sura Najm}

These various examinations make the content (matn) of these hadith (about Ashura fasting) highly suspected and inconsistent with Historical fact, intellectual digestion and Quranic principles which is the only infallible principles other reports should be judge with.

PROPHET WEEP FOR HUSSEIN

Sheik Nasirudeen al-Albaani records a sahih (authentic) hadith (narration) of the holy prophet in his ‘Silsilah Al-hadith Al-Sahiyah’, vol. 2 pg 462 hadith 821:

"Jubril came to me and informed me that my Ummah (nation or community) will kill my son, Hussain. I asked: ‘This Hussain?’ He (Jubril) replied: ‘Yes’ he then brought me some soil (tur’ba) that was red.”

Narrated by Umm al-Fadhal bint al-Harith that she went to the Holy prophet (s) and said: ‘O prophet, I have seen an unclear dream tonight.’ He (s) asked: What is it? She replied: ‘I saw that as if a part of your body was cut off from you and was placed upon my chest.’ He (s) said: ‘You have seen something good. In sha Allah, Fatimah will bear a baby boy and he will be upon your chest.’ So Fatima gave birth to Hussain and he was on my chest as the prophet had notified me. On one day I went to the Holy prophet and put Hussain on his chest then he turned his face to the side and I witnessed his eyes flowing with tears. I asked: “Prophet of Allah (s), may my parents be sacrified for you, what is wrong?” He then mentioned it (the above hadith – “Jubril came to me and informed me...”).”

Similar authentic narrations of the same genre can be found in: “Fadhail Sahaba” by Imam Ahmad ibn Hanbal, vol.2 pg. 965 Hadith1357; “Musnad Abi Ya’la”, vol. 6 pg.129 Hadith 3402; Imam al-Haythami in his ‘al-Majma zawaid, vol.9

It is worth noting that:

1. Imam al-Husayn (alaih Salam) is referred to as the son of the Prophet (salallahu alaih WA a'alih) just like Quran refer to him and his elder brother Imam al-Hassan, (alaih Salam) as sons of the Prophet {sura al-Imran: 61}.

2. Therefore, those who killed Imam al-Husayn killed the son of Prophet Muhammad (salallahu alaih WA a'alih)

3. The Ummah as a whole is accused of the murder of Imam al-Husayn. In particular, all of those Muslims alive at the time of the Karbala tragedy.

4. The Prophet wept for Imam al-Husayn even before the incident happened.

5. Interestingly, the land of Karbala is referred to as the turbah of Imam al-Husayn (تربته). This is a huge virtue for that blessed land.


Hussein (as) speaks!

the book Fadail as-Sahabah of Imam Ahmad b. Hanbal, vol. 2, p. 675, # 1154, there is this sahih Sunni hadith:

Narrated al-Rabi' b. Munzir:

Husayn b. 'Ali used to say: "Anyone whose eyes are filled with tears for our sake, or tears drop from his eyes for our sake, Allah the Almighty, the Most Glorious will reward him with the Paradise."

Link: http://islamport.com/w/ajz/Web/2294/1170.htm

The report has an absolutely sahih sanad.

Conclusion

In Summary, There are Three views on Ashura:

1. Prophet fast and enjoyed the Muslims to do so because he saw and followed the Jews fasting, hadiths claim. How is this kind of hadith stand to reasoning when:
# {Allah warn the prophet never to follow the Jews and christian in their practices."} [Quran 2:120], {Allah testify that His prophet only follow and act on inspiration from His Lord}[sura Najm:1-5}

2. It is a day of joy, blessing and celebration because Allah blessed all of His Prophets on that day.

# {There is No basic evidence for this claim; and how was Muhammad, the leader of all Prophets, was blessed on that day if at all the claim was genuine?!}

3. It is a very sad day because the prophet's son, Hussein, and 73 of his household and loyalists were massacred on the plain of Karbala in the 61A.H, by the same followers who claimed to follow the Prophet.

# {Prophet weep profusely for this day before it even materialized, several hadith reported}

The choice is yours!!!

This is informative and educative. Still skeptic about it though. I thinks it's time I make my research. Once again may Allah increases you with knowledge. Sincerely, I like it.