Are fixed deposit rates different for every bank?

Yes. They are. Different banks offer different interest rate and to different type of customers. Like, senior citizens may get higher interest.

Yes, generally..it's not decided by RBI but by the Bank itself..

The banks may independently decide what interest rates they want to offer to customers.

The banks may independently decide what interest rates they want to offer to customers.

Yes for every bank and even for different time period, FD Interest rates vary. Check More @  https://www.bankbazaar.com/fixed-deposit-rate.H T M L

Yes, there may be a slight difference for fixed deposit rates offered by banks. I suggest you check out the rates offered by DBS as I feel it will give you a lot of flexibility. You will get details on their website.