Use 24v Batteries to run 12v System... Possible?

TV set itself shouldn't be a problem.

Other 120V appliances, OTH, drain battery very fast. Toaster, coffee maker, microwave, hair drier. Some of this (or most?) can be eliminated and/or replaced with propane. It boils down to habits and preferences.

Solar should be planned for worst case scenario, estimate your needed wattage of the array and then add 30-50% to this number. Panels are cheap these days, especially big 230-260W ones, no need to skimp on it.