1. When using campgrounds that do not have water at the site do you fill up before leaving home or does the campground have a spot to fill up when you get there? Or do you just run a long hose to fill up from the nearest water?
The answer is: Yes and yes and yes. Be prepared for any event if you are visiting an unknown campground.
Except for some exceptions, every campground will have water somewhere. If making a reservation on-line, the reservation system will provide information if the site is full-hook up, Water, or Electric only, etc.
In Indiana, most state parks have a single spigot for a group, and the water spigot is shared, meaning you should not attach hoses directly to them. Some state parks are switching their single spigots to non-threaded spigots so hoses cannot be attached. In all Indiana State parks, there is always a common water fill station available. Most fill up when they first arrive because they travel with empty tanks.
I carry a 35 gallon container of water in the bed of my pick-up now, all the time. And we keep about 10 gallons in the fresh water tank so we can use the bathroom when traveling.
Once at the park, I fill up my fresh water, never hook up with the hose, even if the spigot is available. I use my fresh water tank always.
2. Do you ever leave one campground headed for another without emptying your black/gray tanks? We are planning a week long trip in June with stays of about 2 nights each in three different campgrounds the one in the middle looks like it will have full hookups.
If there is a dump station, we always use it when we leave any campground, regardless of how much is in my tank. If the site has full hook-ups, we dump in the morning before leaving, regardless of how much or how full or empty the black tank is. I can back-flush my grey water into my black tank and flush it out without having to use my black tank rinser and my black tank does not have to be full when I back-flush. So it doesn't matter how full or empty my black tank is, the back flush always cleans everything out. And I usually back flush 3 times if I have enough water in my grey tank.
Normal camping, I dump my black tank every 2 days, so I can back flush with the shower (grey) water and not over fill my Barker tote. If on full hook-up sites, I'll flush the black after 6 showers, regardless of how much is in the black.
3. does backing get easier? I pulled a popup for almost 20 years but this new trailer is a different beast. I have taken it out to the local college parking lot three times now to practice backing up and such.
Backing a trailer is a different experience for every person, and every tow vehicle and length of trailer creates a new experience also. Overall, the shorter the trailer, the harder they are to back up, because they respond and over respond to even the slightest steering wheel movement. Longer trailers are easier because they don't respond as fast.
In time, you will figure it out. It just takes time to learn the limitations of your unique rig.
Conclusion:
Congrats on the new camper! Hope you have many successful and happy experience and travels with it!