My question goes thus, to those who have the knowledge, have earned with it and have gained a lot of information
on it or anyone that can help on the topic. Please is java and c family are on the same level, when talking about what they can do.
Like most of what I've
been thinking are as follows:

C used for - Memory, System, Utility in short deals with system programming (let me use that word)
Java - Organization's stuffs like payroll and desktop programs etc.

Please explain what I don't know, can java do what c and c++ do, and is there any abilites java can't do and c family
can do.

yup

Java cant acess memory directly. The other languages can thru pointers.
The other languages can tell you ,programmatically,the size of a data type, java cant.
For feature by feature comparison and differences, google is your friend.

memory and speed differs

Lets use car analogy, java is like automatic car while c/c++ is manual. In java a lot of things are already done for you saving from the stress of implemeting them but giving you less choice and less control. That is the reason while the standard java library is colossal. In C/C++ just the basics are done for you leaving you to take control and make your own choice, which can introduce nasty bugs due to silly mistakes. But the truth that is not told to most beginning programmers is that C++, in particular, has third party libraries that provide aboundant functionalities to save you the stress of implementing somethings youself.

And finally, java virtual machine is written in C/C++ ( correct me if I'm wrong)

If you want to write an operating system, device driver or a real-time video game, you need C or C++.

But for most other tasks in computing, (e.g. internet servers/apps, desktop applications, distributed computing, etc), I think Java is performant enough, and also substantially safer (easier to write bug-free code) and requires less time to program the equivalent task than in say C or C++.