Found the second set of questions:
1.) Is it expensive to have an electric hookup?
Hookup is included in the cost of a RV parking place in a campground or RV park. Difference between a tent site and RV site might be $2 to $5, but a lot more is involved than electricity, it is about the space used, parking pads, patios, etc.
In a long-term site, you might pay the power company for electricity used, rather than a flat fee. Rates are usually those for residential service and they vary all over the country.
2.) How much does it typically cost just to stay overnight at a campground? Aren't there more places to park overnight besides parking lots and campgrounds?
In the parts of the U.S. I've traveled, I've averaged about $20 a night, because I tend to choose the least expensive places. I've been in city campgrounds and at fairgrounds with rates from FREE to $30 a night, $5-10 is typical. RV spaces in Federal campgrounds and state park campgrounds I've seen $12-$40 a night, although there are some really special places much higher (on the beach), I plan for about $16-22.
I've been in RV parks and resorts with fees as low as $16 a night and over $100 a night (destination resort) but I look for the places that run about $25-40.
Other than parking lots (not always legal) and campgrounds, there are rest stops, truck stops (sometimes welcome), on the street (seldom legal) and in dispersed camping areas on public lands (not any public land, there are designated places, and sometimes fees for land use).
3.) Can you take showers when you're on the road and not near a campground?
Yes. If your RV is "self contained" you can shower anywhere you can stop. Self contained means you carry your water and power supply with you (whether batteries, generator or combination of both) and you carry your waste away.
6.) Do most motorhome's get good gas mileage? How much on gas do you spend monthly (and how many miles driven)?
Good compared to what? Not as good as a compact car or mid-size sedan, but better than a 80,000 tractor trailer rig or an inter-city bus (unless your RV is a converted inter-city bus. The right motorhome can give better mileage than many people get in their large SUVs.
MPG ranges from 18-22 possible with a small diesel B motorhome (van conversion) to less than 6 MPG in a 50,000 pound 45-footer (bus conversion). 7-10 MPG is pretty typical in between.
I don't measure my fuel use by month, I only use fuel when I travel. When I'm traveling, I like to move 200 to 400 miles a day, $75 to $150 when gas was between $2 and $3 a gallon.
Historically, I've bought 3750 gallons of gas for my motorhome at a cost of $9850, to move it about 32,000 miles over nine years. The MPG calculator says that is 8.2 MPG. The motorhome is a 30-foot type C, that is a big rectangular box on a beefed up van chassis.
Most boxes this size get about the same fuel mileage. Bigger ones do a little worse, smaller ones can do much better. Thus that efficiency definition I gave you earlier, no more RV than you really need.
I would like to buy a used, but quality motorhome (so I don't have to continuously spend money on repairs) to use as I figure out future plans. I have two dogs that would travel with me as well. What about buying a very small piece of land somewhere with a very small annual fee and somehow having a water supply connected? Are the main fees essentially gas, food, and insurance?
The RV sitting on a small piece of land with utility hookups is a seldom realized dream, because of building codes and utility company rules, but there are some places where people get away with this. They usually dig their own wells (or carry in water), make their own power, use rural waste disposal methods. I'm somewhat familiar with the culture, they don't shower every day and use the Internet, it is often more of a "homeless" lifestyle. Some people do this on the street in large cities, it is not always legal, but they move enough to stay ahead of the police. Places where you can do this can be hard to find, and have been disappearing as county governments adopt urban building standards, and cities work harder to get the homeless off their streets.
You talk about "fees." The main costs are not fees, the costs are costs of money, costs of land, costs of services (like insurance) and costs of energy. The less you use of money, land, energy, services, the lower the cost. Take this minimalist lifestyle to its logical end, you would be out there with my late baby brother, sleeping on the sidewalk with his trash bag of spare clothing and other possessions.