Yes. In fact that's what I use it for.

The instructions that come with the unit state that it shouldn't be used on anything that has a heater, so a portable heater would definitely be out.

YES! Works great will not do anything to car battery as you are driving.

The instructions that come with the unit say that you shouldn't use it to power anything that has a heater, so that would rule out a hairdryer.

There should be a label on the pump. It should say how many watts it uses, if it’s less than 250, then yes.

Absolutely!!!

Yes, of course, it's no different than any other home electrical outlet in your home.

There's a link at the bottom of the product's web page "Length of warranty: 12 Months SEE DETAILS".

This is a power inverter. You plug it into a 12v power supply such as your car power port, and you can immediately use the AC120 Volt output. There is no battery in this, so it doesn't require any charge time, and will not work if not plugged in.

Yes, it will provide continuous power to the laptop but don't expect it to recharge any laptop battery.