Deposit of money in bank

Yes, upto "saved money"

Any amount can be deposited into bank on  producing proof of identity. (Pan, Aadhar card etc)

If you have got as gifts - Gift OR other income OR some suitable field may be opted. 

I don't think bank will ask for Proof of Income. It is not Bank's duty. Just quoting your PAN (and Copy of it) will do. 

I hope, being a student you are not going to deposit in lakhs. (if its more than lakhs - you must be having Source for such Income. 

Thanks.