Well, microwaves are usually rated by the output power of the magnetron (the "cooking power"), rather than by how much power they draw. An "800w" microwave will generally draw at least 1200w. The exception is the WaveCube which the marketing says is a "600w" microwave, but that's how much it draws - it only has a 300w magnetron.
Coffee pot...I actually have no idea how much they draw, I make coffee on the stove.
Power tools...
Most won't draw over 15a of 120v, which is 1800w. However they usually have a pretty hefty surge load needed to start them. Something like a 1500w inverter with a 2500w-3500w surge rating will run most of them. A few, like some Skil saws and chop saws, need a bit more.
Some battery tool chargers will have problems with Modified Square Wave inverters. I have a Ryobi kit, which came originally with 1 charger. The guy I bought it from gave me two regular (120v) chargers and also the one that plugs in the cigar lighter. I suspect he toasted the first charger with a MSW inverter, then bought another one and toasted it before he finally bought the lighter plug charger, but I can't say for sure since he didn't tell me when I bought the kit that the 120v chargers were burnt out...
As far as I know, the newer DeWalts and Milwaukees (and some of the older ones), and all the Makitas ever made will work fine with MSW. You should definitely check into it before you try it.
For the most part, just about everything will work fine on Modified Square Wave, but a few things won't and you usually don't know exactly which things won't until you try them and burn them out...
Some microwaves and washing machines will burn out their control boards on MSW. Motors, like power tools and fans, will work fine, but will usually hum a bit.
Cheap MSW inverters will have a truly square wave, while better quality ones will have a wave that looks like stair steps. The really high quality ones will usually have a bunch of steps. The ones with a bunch of steps are sometimes referred to by the marketing monkeys as "quasi sine wave".