When we hear of this type of trip, we think of walking. You may be talking about using trains and other forms of transportation.

I don't use a pad. The best way to find out if you need one is to sleep outside without one and see what happens.

It's late in the planning to ask about sleeping outside. The only fear I would have in the United States is from law enforcement. To avoid detection, make camp after dark and break camp before sunrise. Don't use any lights.

Cross-country walkers often ask people if there is a place they can set up a tent for the night. In the United States, people often invite them to their homes. It's possible to cross the United States on foot with almost no money as people want to contribute to the adventure. With some practice I think a person could end up with more money than they started with.

Your trip seems to be a spur of the moment adventure. These are frequently successful, so enjoy the trip and have fun with whatever happens. Don't let anyone tell you it can't be done. It can be done because others have done it.