Often when your credit has improved, market rates have fallen, or you have paid down enough that the loan is worth less than the car. Check the total cost and the fees, not only the monthly payment.

Usually, yes. A longer term spreads the balance over more payments, which lowers each one, but you pay more interest in total.

A new application can cause a small, temporary dip in your credit score. Applying with several lenders within a short window is often treated as one inquiry, but check how your lender handles it.

It can be harder, because lenders often limit loans to the value of the car. Ask lenders directly what they will offer before you apply.

Some lenders charge none, and others charge an origination or title fee. Ask for the full cost of the new loan, and compare it with the interest you would save.