A mortgage modification changes the terms of your original mortgage agreement. Your lender will work with you to try and find a way to lower your monthly payment by adjusting the terms of your current mortgage. The goal is to help you get back on track.
Generally, once you've locked in a mortgage rate, the terms are fixed and usually cannot be renegotiated. However, some lenders offer a float down option, allowing you to negotiate mortgage rates if market conditions shift favorably during the rate lock-in period.
There is technically no limit to how many times you can refinance your home. If you meet the lender's qualifications and it makes financial sense for your situation, you can refinance as often as you wish. However, just because you have the option to refinance multiple times doesn't mean it's always a wise choice.
Strictly speaking, a modification to a mortgage does not need to be recorded to be enforceable between the borrower and the lender, as they are bound by the modification as a matter of contract law.