What an extra payment a month is really worth.

Paying extra principal is a guaranteed, tax-adjusted return equal to your interest rate, with no volatility. Investing has a higher expected return and no guarantee. At a 3% mortgage the maths usually favours investing; at 7% it is much closer, and the certainty starts to matter. The honest answer is that it depends on your rate, your tax position and how you would actually feel in a bad market — which is a different question from which one has the higher expected value.

Not always, and this is worth checking rather than assuming. Some servicers apply extra money to the next scheduled payment instead of to principal, which gets you nothing. Make the extra payment separately, label it as principal-only, and then verify on the next statement that the balance actually dropped by that amount.

Usually PMI first, because it is the cheapest win available. PMI is pure cost that buys you nothing, and reaching 80% loan-to-value removes it permanently. Getting there often takes far less than you would expect, particularly in a market where values have moved. The loan-to-value calculator shows you exactly where the threshold sits and when you cross it.