Sorry Ash for the late reply. Been outta town for the last week.
Looks like you've got it covered. The Honda will run both the fridge and window rattler, expect it to groan a-bit if they both wanna run at the same time, but it will do it and be fine.
Don't worry about start-up amps/inrush current. It's such a brief thing that it becomes negligible.
My experience with the everyday 19 cu ft fridge is that they draw around 7 to 9 amps when the compressor is on. So 9 amps (1080 watts @ 120v) and the ac at 6.1 amps (732 watts) = 1812 watts. The Honda will let you know it's under load, but it will run like that all day and be ok. You'll still have enough power to run a tv and a light or two.
I would recommend a 12awg extension cord minimum from the gen to the house, but you could then split it up with smaller cords to different things and it'll be fine. If the gen is further than 50 or 60 feet away from the appliances, a #10 awg cord to the house would be better, but a 12 awg will still work. Use only enough cord, don't go real long if you don't have to, and don't 'neatly' coil up extension cords when in use. That creates heat and compromises amps. Just lay the cords on the floor like a dead road snake.
You're a smart guy, and they make all this stuff for the stupidest people, so you'll be ok.