The more I read, it is painfully obvious that there is more to learn

I am planning on leaving on a trip South in about a week and so I want to plug in the heat tape for the travel to help ensure the water lines don't freeze. As it doesn't take a lot of power I assume I can use the inverter to power the heat tape?
Secondly, when the inverter is on I believe the engine alternator charges the house batteries so as to keep them charged. Correct?
Third, the manual is not specific other than stating that the inverter will power TVs, Microwaves etc. Are there specific things it will operate and some it won't or is everything powered, except for the fridge and

?
As you can tell, I haven't hardly used the inverter - to date either the MH has been plugged in, able to run the genset or just quick overnight so the batteries ran the lights, heating fans.
Thanks,
Jeff