On a standard fixed-rate plan, yes. Income-driven plans and some other options change the payment, so check which plan you are on.

It depends on the rate you pay and the return you could earn, and on your other goals. Paying extra avoids interest at the loan rate, so it earns a return equal to that rate, before taxes. Investing carries risk.

Check with your servicer. Most apply extra money to principal when you say so, but some apply it to future payments unless you tell them otherwise.

Calculate each loan separately, since each has its own balance and rate. Then decide which one to target first.

Your loan servicer's online account or the latest statement shows both. Use the current balance, not the amount you first borrowed.