Howdy Comfun1. To get more accurate answers to your questions, a little more info would be needed.
I think you need to know your amps required (these should be on a tag on the back of your TV and satellite receiver) for everything you plan to run off the inverter at one time......in order to size your inverter correctly.
You would also need to know the battery you are using amp hours rating, to see how long it could run the inverter (and it's corresponding load)
There are all kind of online calculators out there, to help you configure your power draw, once you know all the combined total amps for everything.
Maybe someone will provide a link to their favorite one.
2011 Flagstaff 831 RLBSS
I used to be addicted to time travel, but that's all in the past now.