I know that Fed doesn't set mortgage rates directly, but they usually follow Fed's policy. My question is: How soon do mortgage rates go up after Fed's rate hikes, and do Fed rate hikes affect all mortgage products (10, 15, 30-year terms; both fixed and ARM), or only some (like only 30 years, for example)?
Banks change loan interest rates whenever they decide to change them, driven by two opposing factors: the need to make a reasonable profit, and the need to not lose too many customers to other banks.
Generally, what this means is that each bank wants a certain minimum amount over the prime rate, but is held fairly close to that minimum. Note that the minimum may reflect how much they trust that the loan will be repaid; it is possible for credit rating to affect interest rate as well as whether you can get the loan at all.
But there is no specified time at which the rate changes unless it is specifically advertised as some percentage over prime (in which case it probably happens immediately).
If you expect the rate to change, many banks will let you "lock" the rate on a loan application for some number of weeks.That protects you if they increase rates during that period.
This is generally true for all new loans, not just mortgages.
You may not see a change in mortgage rates just because the Fed increases its borrowing rates.
Base Mortgage (i.e. 30-year) rates are set by the overall debt market which buys and sells government debt based on expected future interest rates. So in a sense, the recent rate hike was possibly already included in the 30-year Government rate. That rate would only go up or down if the actual rate change was different than market expectations.
Retail Mortgage rates are based off of this base rate plus a spread to account for risk of default (e.g. higher-risk consumers get higher rates) and to generate a profit for the bank.
Another layer that's in play with mortgage rates is the Mortgage Bond (Structured Debt, MBS, etc.) market. That's basically the marketplace where investors buy and sell existing mortgages. The prices that investors pay for those bonds can also have an impact on retail mortgage rates.