WELCOME!
Here are my answers to your specific questions. Keep in mind these are specific to the way my family does things. There are many, many ways to skin the geocaching cat [].
1. An emphatic NO! It is not cheating to read the clues and location vicinity of the cache. That's what they are there for. Since I use Geocaching to take me to new places, I almost always read the clues beforehand. You may want to try it both ways and see which is most fun for you.
2. I've done both. I've started out with nothing but the coordinates and used the GPSr to search for the right roads, etc. I've also plugged the coordinates into a mapping program to get a general idea of which roads to take. Had fun both ways, but the former seems to be most satisfying afterwards.
3. We ALWAYS go caching as a family (4 of us + 1 dog). I always work the GPSr; my daugter (11) reads the compass; my wife reads out the description, clues, and logs from the cache page printout; and my son (15) usually ends up finding the cache. We've never even thought about needed a 2nd GPSr.
4. I don't use a paper map for the cache hunt. Whether or not I have one with me depends on where we're going. In a local park, or in some other civilized place there's usually no need for a map. If we're going to be hiking a trail though (we do a lot of non-geocaching hiking) I try to always have some type of map (usually a TOPO) with me purely as a safety precaution. It's one of the 10 essentials for hiking.
Hope this helps!
Wayne