Some basic questions?

I am a beginner in golf technicalities. Since I bought my beginner set 3-4 months, I have been just playing with some buddies... like grab your clubs, go to the course, grab some beers and start hitting. My scores are around 105-110. I realized that I have been hitting the clubs pretty much like baseball, without giving a thought about the technique. I have found that I am very consistent with the irons; I can hit a 5-iron 150 yards straight, but horrible with the woods. Now I have decided to approach the game from the techniques standpoint and get my basics straight.

So here are some questions...

1) Terms: What is lie, takeaway, cut on the rough?

2) I am 5'10" and 175 lbs. What size clubs should I use? Does everyone play with the standard size? What are various club sizes for irons and woods?

3) I have $120 beginner clubset (Knight Electra). What are some good brands around $250-300? I don't want to spend too much till I get a good feel for the game.

4) I want to buy a utility wood, since it is shallower and easier on the fairway. Please recommend something not very expensive.

5) What exactly is a strong grip? I fade/slice (unintentional) too much with the driver. So people on the web told me to use strong-grip. But if I shift my grip a bit towards right to make it strong, my right hand goes under the club if I want to keep the club square at address, and I still end up slicing/fading the ball unintentionally. If I shift my grip towards right, but then re-adjust my wrist so that my right hand does not go under the club, then the clubface is a bit closed at the address. But the latter has helped me to hit the ball straight. Am I still doing something wrong?

6) Is it common to get calluses on the 4 top mounts on your palm? Or does it indicate my grip is wrong?

7) On the downswing with the driver, sometimes, I totally miss the ball or the clubface hits the ground way back and all the power is expended and the ball just moves a few feet or the clubhead strikes the ball at a place other than the clubface. This happens though I have worked a lot on my backswing after reading too many books. Is it happening because my right elbow is not staying connected to the body or wrists are moving during the downswing? How to correct this problem on the downswing?

I'll be back with more questions the next time after I try your tips on the range this week. Thanks guys.