1) Not necessarily, no. In low power situations you can use a battery bank and solar power and do just fine with that. Others will chime in with info/specs if you're interested in that. If you're not interested, then yes, it will have to run anytime that you want power. You can install 12v lights and run those off the starting batteries but that would be about the limit.
2) I'm going to assume that you mean Onan, and not oman. If that's the case, what you have is a pretty good unit. I'd look at repair options before I'd replace it because it's going to cost you many 1000's $ to replace it with a similar quality unit.
3) Wattage depends on power usage. 7000 would be plenty for most people on here. You'll have to look at all of the usage items that you'll be using/installing in the bus and go from there. AC units require a lot of power, as do microwaves, electric stoves, electric heaters, etc. Get a list and we can help you from there.