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EV is simple. If you're 70% to win a $100 pot, your EV is $70. If you're 50% to win, 10% to tie, 40% to lose, your EV is $55.
Fold equity is the value that your hand gains when you bet. Suppose you're up against a tight player who usually folds marginal hands to a raise. You have 42, he has T7, so you're about 30% to win right now. But if you bet, you will gain fold equity, and might be around 80% to win (because he will often fold, and even if he calls you're still 30% to win).
Read this for more info:
http://en.wikipedia.org/wiki/Fold_equity
cEV is pretty unimportant. Almost all of the time, your cEV will be the same as your regular EV.
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Your cEV is nearly always *not* the same as your $EV unless you are playing a cash game.
In an MTT early, they're pretty close.
It's curious that you mentioned SNGs, because in a standard SNG, cEV != $EV until you are heads up. That's easily demonstrated by considering this:
Ten-player $10 SNG, payouts 50, 30, 20. All four players have identical stacks of t3750. Player A and player B check flop and turn, and get their chips all in on the river. Player A shows the nuts and doubles up. His chips double but his dollar equity cannot (his equity can never be more than $50 because he can never win more than that). His cEV when called on the river was (a bit more than) 100% (more than it because he stood to gain two blinds already in the pot as well as his even-money bet), but his $EV is not.
Interestingly, the other two players had no cEV at all, because they did not play the hand, but both gained $EV.