@Kabuku find out if the microwave is on an arc-fault breaker. They are notorious for nuisance tripping. I had the problem with a 10year old GE fridge. There is a $1.49 fix: a grounded-to-ungrounded adapter plug. NOT for fixes in or near the sink.
@Kabuku The virtue of that cheapo plug is isolation from ground and arc fault sensitivity. Appliances you could possibly touch with one hand while the other was grounded by, say, the sink must not be isolated. But a microwave NOT near the sink is OK.
@Kabuku In fact, the Youtube how-to for this kind of breaker tripping explained much pricier fixes. My fridge would be on dedicated circuit had the house been built to code. but instead of changing out the breaker I HAD to isolate the load: shared line.
@Kabuku Good Luck. Not much to loose. I should add that an observed failure mode for microwaves [i.e. OURS did this:] dead short , probably in the power supply. Proved by touching ohm meter to various places after removing the cover.
@Kabuku The disposal MUST have GFI, The rest of the outlets in a kitchen /should/ be GFI but the breakers cost up to $50 and putting a GFI breaking outlet between breaker box and string of normal outlets is legal and cheaper.