Fly Fishing Beginer - few questions

[draku007]

Hello everyone,
Just like the subject says I'm a fly fishing newbie who switch from spinning to fly. I first try fishing with flies but had no luck, didn't know how to cast and where to look for a fish. Moved to fly-rod with worms and had some luck. Upgraded to fly+nymph setup and had some luck mostly catching fish on a nymph (got only 1 brown on a fly using fly+nymph setup). The one brown was caught on adam's fly and it was by far the most exciting fly fishing experience so far. Watching the fish going for my fly and making a splash... ohh yeah.
I think I already have the basics and I know where to look for a fish but I haven't had much luck fishing with floating flies. So here are few questions I have for you:
1. Is using fly+nymph setup common practice or would that be considered "cheating"?
2. If a fish is biting a nymph on a given day, will the fish also go for a floating fly and it's all about the correct fly pattern?
3. Is nymph that much better than floating flies or is it just what I got used to and what I "mastered"?
4. Several times I saw a fish going after my fly and turning back. Is there a simple answer to it? Should I change my fly at this point?

I'm fishing mostly on Pequannock river as it's my local water.

Thanks for all your help,
Jim

PS: I lost a nymph on Saturday morning after my first cast. After further inspection I noticed that the nymph has untied (need to work on my tying skills). I went to the same place on Sunday evening and pull out a rainbow with my Saturday's nymph in his mouth.