The honest way to think about a fixed rate is that it prices an option, and the borrower is on the good side of it. Over thirty years, market interest rates will move a long way in one direction or another, and on a fixed-rate loan the lender absorbs all of that. If rates rise, the lender is stuck collecting the old rate on money that has become more expensive. If rates fall, the borrower is not stuck at all, because a mortgage can be refinanced. So the lender bears the downside of rate movement and does not keep the upside, and it charges for that asymmetry in the rate it quotes. This is why a thirty-year fixed rate typically sits above the introductory rate on an adjustable loan of the same size to the same borrower. The gap is not a discount the adjustable borrower has found; it is the price of the certainty the fixed borrower has bought.
Two practical consequences follow. First, comparing a fixed rate to an adjustable loan's initial rate compares a price to a teaser, and the honest comparison is between the fixed rate and the range of rates the adjustable loan could reach under its own caps. Second, a fixed-rate borrower who watches rates fall well below their own has something to act on, since refinancing converts the option into money, subject to the closing costs of doing it.
Fixed fixes the rate, not the payment, and this catches people every year. A mortgage payment usually collects principal, interest, property taxes and homeowners insurance together, with the tax and insurance portions held in escrow by the servicer and paid out when due. Property tax assessments and insurance premiums move on their own schedules, so the amount leaving the borrower's account can rise on a loan whose interest rate is, correctly, described as fixed. The escrow analysis that produces the increase is an annual event and has nothing to do with the note rate.
The term is a separate dial from the rate, and the trade-off is genuinely person-specific. A shorter term means a higher monthly payment, usually a somewhat lower rate, and far less total interest, because the balance spends less time outstanding. A longer term means a lower payment, more total interest, and more room in the monthly budget for everything else, including saving. Neither answer is right in the abstract. What is worth knowing is that the difference in total interest between a fifteen-year and a thirty-year loan is large, and that the flexibility of a lower required payment has real value to a household whose income is uneven, since extra principal can always be paid voluntarily but a high required payment cannot be reduced voluntarily.
Paying extra shortens the schedule; it does not reduce the next payment. This is the most common misunderstanding of a fixed amortizing loan and it belongs here rather than with the amortization mechanics, because it is what fixed actually means in practice. The note obliges a fixed payment each month. A lump sum applied to principal reduces the balance, so less of every subsequent payment goes to interest and more to principal, and the loan finishes earlier. The payment itself stays where it is unless the servicer agrees to recast the loan, which some will do for a fee. A borrower whose goal is a smaller monthly obligation rather than an earlier payoff needs a recast or a refinance, not a prepayment.