I am also a student and applied for naturalisation in April. I applied through a nationality checking service, and brought a letter from my university confirming my student status and my student ID card to my appointment. As far as I could tell, it was simply to provide confirmation of my occupation. They used my (also non-EEA) passport to establish that I met the residence requirement. Since we are not from the EEA, our physical presence in the UK is established through passport stamps.
These were the documents that my NCS caseworker checked at my appointment (I was applying as the spouse of a UK citizen):
- Both of the passports (1 current, 1 expired) that I have held in the last three years.
- My biometric residence permit showing my ILR.
- My marriage certificate.
- My Life in the UK test pass letter.
- My husband's passport.
- Letter from the university at which I am currently studying, confirming my student status.
- My university student ID.
It doesn't sound like you will be applying as the spouse of a UK citizen, so (3) and (5) won't be relevant to you. I am also exempt from the language requirement. If you are not, then you will need to provide evidence that you fulfil it.
If you have other documents that establish your physical presence in the UK, it can't hurt to send them (or bring them, if you're using an NCS, which I recommend you do). If your caseworker doesn't think they're necessary s/he can set them aside, but I think it's better to have too much evidence than to risk potentially having too little.
ETA: I've just noticed that your post and posting history indicates that you are also an EEA citizen and have permanent residence, not ILR. These two things are not the same. If you have PR, then the letter from your university verifying that you've studied there is probably mandatory. You may also need to show that you have been living continuously in the UK for six years instead of five.