1. It varies by campground, contact them to see what is available. Some have spigots every 3 to 4 sites (keep a couple hoses in the basement), and some only have the fill station near the dump station.
2. Gray water can be dumped pretty much any time you want, but the black tank needs to be pretty full so all the "stuff" flows out completely. Just have to keep an eye on it and decide as you go.
3. Yes, with experience. What you are doing is the best way to learn. Get some obstacles (traffic cones/buckets..) and practice backing between/ around them. It's all about seat time.