Re: casting techniques
It sounds like a couple of problems. One, if the line isn't shooting because your hands are wet, you likely don't have enough line speed. If you have slack between line hand and stripping guide on the backcast, again that is likely a line speed issure.
Or, it could simply be that you haven't yet got enough line mass out of the tip yet to shoot line.
Depending on what kind of fishing you are doing, if you work the area close to you first, then gradually increase your range, there may be no reason to strip the line in so far on successive casts. If the previous x number of short casts produced no fish, there is little reason to continue stripping though that area.
Then you can simply increase your range so that you can pick up enough line after stripping through the area you're fishing to make whatever change of direction is needed and shoot it back out again.
If you are fishing big water, a stripping basket may help you with the line fouling problem also.
Still-water fishing of shorelines from a canoe or boat is a great way to develop a good feel for how much line you can comfortably pick up, re-direct and then lay down without false casting. Then you don't need to worry about obstacles behind you and can get some solid practice/experience with less frustration.
As Silver said, learning to shoot into the backcast will help enormously in keeping you fly in the water more of the time. And as Ard said, false casting to dry off flies is best done well away from where you intend to present and drift the fly.