It is a pump for a well, 485ft down. I don’t want to risk any damage to the pump, as it is expensive to replace.
If this supplies enough power can I use a 1200 watt (3000 watt continouse) voltage inverter clamped to a car battery connected to a 120V>240V adapter? Can the pump safely be run on 120V? If I get a generator that produces 120V (if the inverter is not good to use), can I use a adapter to get the 240V or will I need a 240V generator?
Sounds like your situation is similar to mine. Ideally, get a 240v gas generator with sufficient wattage to handle the pump. Honda makes some nice portable ones in various wattages, I think. Using a battery/inverter arrangement, less good – what happens when the battery runs down?
Fersure, don’t run a 240v appliance on a 120v supply. It might work at first, but it’ll burn it out eventually.
Also, very important – don’t forget to wire up the pump-powering arrangement so that you don’t feed power back into the utility lines during a power outage. Imagine what happens if the utility crew fixing the wires grabs one coming from your house!
Some of my neighbors have a big switch in their garage just for this purpose. When the power goes off, they flip the switch, fire up the generator just outside the garage, and their pump and refrigerator is back in business. So if you are going to make this wiring change, consider including the critical appliances (like your TV 
) on the separately-powered feed.
120V>240V transformer of sufficient capacity. Yes.
No, no way.
Again, a transformer is what you need and, yes, it will work although if you are going to buy a new generator you might as well get one which outputs 240.
So there is no problem with running a pump on an inverter (as for what happens when the battery runs down, I am not planning to run the water that much at a time, plus I can start the car.
It’s just the issue of if the inverter puts out enough power. If I get a generator, I assume a 120V will be much cheaper then a 240V, but I will have to look at the adapters to see if it’s worth it to get a 240V gen.
I’ve heard that a generator running on gasoline is not the best, and should consider running on propane.
How big is the pump motor? A 1 HP motor requires about 6.5 Amp. at 220 V. If your inverter, generator system is 100% efficient the battery has to put out about 120 Amp. The inverter generator will not be 100% efficient. Probably the two in tandem will be a lot closer to 70%, if that. At 70% the battery current rises to 170 Amp.
I wouldn’t even consider it. Buy a 220 V. generator.