Is it possible for a microwave to damage outlets and after a while cause a breaker to pop under load?
It’s funny, when a safety device like an AFCI trips, people are really reluctant to consider that it might be exactly what it says on the tin.
An AFCI breaker detects arc faults - that’s where a wire is either making poor contact and normal current is causing arcing across that poor contact; or; where a wire is partially shorting with another wire (but not flowing enough current to trip the breaker).
A wide variety of wire and device problems can cause arc faults, but top of the hit-list is Backstab connections. And since your house was done hit-and-miss, and very much NOT up to Code, I bet that’s exactly what is going on here.  The person used backstabs on the receptacles, and they are failing either because they are backstabs, or that + poor workmanship.
Since circuits are generally wired daisy-chain (breaker to point-of-use 1 to point-of-use 2 etc.), the core problem can be at any point in the daisy chain.  When the breaker in question trips, survey which sockets lose power - they all need to be checked.  Inspect where the wire attaches.  Obviously you can’t inspect where a backstab attaches (and you don’t want to use them anyway), so firmly twist and pull the wire out of the backstab and look for arcing marks/spots.  Then put them back on a side screw.
Lastly, if the work had been done by the seller of the house, and is substandard (and it certainly sounds substandard for reasons I’ll describe), then the seller owes you a pile of money.  Because the shoddy, obviously non-permitted non-inspected work definitely should have been on the disclosure statements, and was not.  I haven’t done enough real estate to know which of the various insurers covers this (title insurance???) but one of them should; they in turn will go after the seller.  If none do, then you go after the seller.  Shame on them!
Why it seems substandard:  Code requires a bunch of dedicated circuits your house doesn’t seem to have.

A dedicated 20A circuit for bathroom receptacles, that serves no other loads (except if it serves 1 bathroom it can serve other loads in that bathroom).
Two, count em two, circuits dedicated to kitchen countertops, which can power nothing else but a gas range, a clock, or other kitchen/dining area receps.
Dedicated circuits for dishwasher, disposal, built in microwave, and electric range obviously.
There is no requirement for a dedicated circuit for a fridge, but it’s a pretty good idea. Fridges should never be on GFCI/AFCI, for the same reason fire alarms shouldn’t.
Dedicated circuit for laundry room.