1.) What is the most effective system for heating/cooling?
For cooling, you open windows or run a mechanical air conditioner. The air conditioner needs 120V power, which you provide by plugging into the grid or running your own generator.
Most effective heating is fossil-fuel fired, either LPG-fired forced air or diesel-fired hydronic systems. The forced air systems are not particularly efficient by modern standards. Some of the hydronic systems use waste heat from the engine and heat water for you.
Heat pumps provide a more efficient, but less effective, heating alternative. I use my heat pump for much of that part of the year it is not being used for cooling.
2.) If you're in the midst of traveling somewhere, where do you park and sleep until the next day?
I like to stop at campgrounds or RV parks, for which costs might range from free to something more than $50 a night depending on location and amenities provided. I average about $15 but make a lot of stops at low cost public campgrounds, at city or county parks providing this service for transients.
Rest stops, truck stops, and parking lots are an alternative when overnight RV parking is permitted. Even in places where truckers stop, RVs are not always welcome. Walmart is popular because it has a general policy, with local exceptions, of welcoming RVers.
Sometimes I stop at motels for the night. Most have room to park a RV, especially motels catering to truckers and work crews. Motels have facilities I sometimes want, that I don't necessarily have in the motorhome, like unlimited hot water or a sports bar.
3.) Where do you take showers and where does waste go?
I take showers in public showers at campgrounds and RV parks, I take showers in hotel rooms, and I use the shower in my RV. The waste water in my RV travels with my RV until I get to a place where I can legally dump it. Dump stations are found at RV parks, RV campgrounds, truck stops (most OTRs now carry waste from their sleeper cabs) and some gas stations and rest stops. There may or may not be a fee for dumping, seldom more than $5. You also carry fresh water, which you refill at some of the same places.
If you want to shower in your RV, you will learn how to take water-efficient showers. I shower in some of those other places to get a long, luxurious shower from time to time.
4.) How much does it cost for a high-quality RV and what qualities make a highly efficient RV?
I'm not sure what is a high quality RV. I don't know that I've seen one. Motorhome prices (new) range from $50,000 to more than $2,000,000, and while one is bigger, more luxurious, more ostentatious than the other, I'm not so sure that it is made better.
You can save a lot of money buying used. This will also save you one of the biggest ownership costs, which is depreciation and cost of money. It is not unusual to be able to purchase a usable $50,000 motorhome for about $10,000 to $20,000, or a $500,000 motorhome for $100,000 or less.
Not knowing what you mean by "efficient" I will use the general sense, so what makes a RV efficient is a size no larger than you need it to be. Anything more than you need is a waste of materials, energy, and money.
For fuel efficiency, the smaller the better. Most of the fuel is used pushing that box through the air, so the smaller the box the better. Diesel engines in the same size motorhome will give you more miles per gallon of fuel (the fuel is denser) but not always more miles per dollar.
5.) How do you use the internet?
When traveling I use the wireless data plan on my tablet and phone, and I use free WiFi where I find it: restaurants, coffee shops, campgrounds, motels, rest areas, libraries, wired downtowns.
Because my data plan is AT&T, all commercial AT&T hotspots are free for me. I think T-Mobile is another hotspot provider with a similar policy.
I use the Internet for communication. I don't use it for streaming massive amounts of data.
6.) What payments go along with owning an RV, just gas?
Motor fuel is not really an ownership cost, it is a cost for moving the RV. It is the biggest cost of moving the RV, which also includes cost of tire replacement, oil changes, and other chassis maintenance. When gasoline topped $4, cost of moving my motorhome went to about 50 cents per mile.
Ownership costs include insurance, storage, maintenance of the house and house equipment (some types of RV need a lot of attention to structural weakness, notably around openings and along the long seams where the box was assembled). These have run about $1200-2000 a year for me.
The other, potentially bigger, cost is depreciation and cost of money, whether just loss of investment income, or interests costs. My motorhome has lost at least $40,000 in value over 10 years, averaging $4000 a year. The $58,000 I put into it (buying used but nearly new) was earning better than 8%, so the cost of that has been another $4500 or so, and that's forever because the value of the principle has disappeared, to never again be re-invested. Multiply those numbers by 10 for a $500,000 motorhome.
Third cost is cost of using it: camping fees, LPG fuel. The first is per night, the second has to do with how many hours cooking, heating water, heating the house, running the refrigerator. Heating the house uses lots of fuel. You might put the cost of one or two house batteries here, about $100 each every few years, but that could be an ownership cost, because the things seem to die of old age anyway, whether you are charging/discharging them or not.
7.) What are your main concerns and most frequent troubles with your RV?
My main concerns are about maintaining the integrity of the box, so that it does not get destroyed by leaks. That requires frequent inspection and occasional re-sealing, at least twice a year, and it is a fairly expensive job when done professionally, 2-4 hours of labor at rates now around $100 an hour.
Most troublesome part of my RV has been the generator, which I use to run air conditioning on the road when carrying passengers, and to power a few other things when stopped where I have no electrical hookup. This is a problem with all small gasoline engines run infrequently and stored with today's gasoline formulas left in the engine.
My main concern generally is that I don't get enough use of the RV to justify the costs of ownership. $8000 - $10,000 a year just to own it, whether I use it or not, and if I spend 10 nights in it that's $1000 a night. If I spend 100 nights in it, that's still $100 a night.