Hello and welcome to RTA !
You can't just pull up in a Lay-by and sleep in your RV the night unless stated otherwise. There are truck stops and some Walmart's etc have allowed overnight parking but it's by permission of the manager on a one to one basis. The thing is [in my opinion] it's not going to be a whole lot of fun, you can't set up camp, get out the table and chairs and light the BBQ and the Kids won't be able to let off steam running around, it's purely somewhere to rest. Whereas you can get good value State park and private campgrounds with the amenities and generally in nice surroundings, for me that's surely worth a few extra dollars each night.
Water will depend on how sparingly you use it, we [4 adults] have gone a couple of days without topping up and emptying out with no problem, but am not sure how far we could have stretched it. You can use dump stations where you are not a guest in many places but a charge is normally made.
Generators are for use when not hooked up and are charged at an hourly rate for usage. You should only need it on briefly at peak times if you are using extra power like the microwave etc as the 'house' battery is recharged while driving and can run lighting for a while. There are usually quiet hours so that you do not disturb others with noise from it. It operates off the vehicle fuel tank and will not operate if you are under a qtr of a tank to ensure you don't run out of fuel.
Figure on a fuel return of 9mpg on the RV, I can't remember the size of tank but it usually tells you on the rental website. Don't let it run too low though because they guzzle it quick and as said it will not operate the generator if it runs low.
I've not experienced anything other than kindness and helpfulness when travelling in the States, but just like anywhere on the planet, you have your bad neighbourhoods/areas. As a tourist you normally have to go out of your way to find trouble and the simple thing to do is use your natural instincts as you would at home and if some place don't feel quite right, it usually isn't so just move on.