I would say no more than a 1000 watts. But its not going to run much. A small TV or a small microwave. It wont run a frig. The car can run for days as long as you check the fluids. Do not run it your garage. You will be better off to find a generator.
I think 200 watts, tops, your car uses some of the alternator output. Say it’s a 60 amp alternator, that’s 720 watts at peak output. Your car uses some of that, and you’ll get less at idle. Ones you plug into the cigarette lighter are more like 150 watts.
How would you connect the inverter to the car?
And if you have no power, you probably won’t have an internet signal to put through your router.