Please I need an advice on what to do, I submitted an application to get my student permit since September 3 and never hear any outcome yet, does it takes that long? please advice

Welcome to Nairaland!
Yes, it could take that long especially for these three reasons:
1) When the student permit is not deemed too urgent.
2) When they need to do some verification or background checks
3) When they are too busy with other jobs before yours.
   Now, no one can advise you on that, they will get back to you in due course. But for the mean time, it might help if you bother them a bit with letters, emails or other effective correspondence. Cheers!