Check with your lender — some loans apply extra payments to principal automatically, while others require you to specifically mark the extra amount as a "principal-only" payment, or they may apply it to future payments instead. This calculator assumes it reduces principal immediately, which is the best case.
Some loans (especially certain mortgages) charge a fee for paying off early. Check your loan agreement before committing to a payoff strategy.
Not necessarily — it depends on your loan's interest rate versus what you could realistically earn investing instead, plus your own risk tolerance. A guaranteed "return" equal to your loan's interest rate is often compared against expected investment returns when deciding.