2nd question. Is it worth telling the recruiter that I got laid off
just in case he has other jobs available?
I would tell them this, and give them the first day you can start work at a new company.
This can open additional opportunities, because sometimes a client of theirs has an immediate need. If most candidates have to work a notice period that will last weeks or months, then they can't help a company who wants to start a new employee on Monday.
I once part of a group that was given 3 months notice that we were going to be laid off. The company only required that we not leave during the first two weeks, so they could have us document what we were doing. After that we only had to give a single days notice. Some people jumped after a few weeks, others went all the way to the end. It was nice that we could leave at any time. It opened up more possibilities.
Are recruiters generally willing to take you back as a candidate if
you change your mind on it relatively quickly?
A quick change of status is fine. That means that the position is probably still available. If you waited weeks or months it is likely the job is gone, but they still might have others you could qualify for.