Hey Thisapear,
1.) That was answered pretty well by la55i already. Every format can be played profitably, so the choice is up to you. It should be mentioned, though, that while the variance in SNGs is generally higher than in cash games, your losses in this format are capped, which can be advantage if you tend to suffer from tilt during bad runs. Whatever you choose, just keep in mind that not everything that works in a cash game will work just as well in tournament poker, and vice versa.
A starting bankroll of $20 is pretty low to take swings in either format, so I guess MTTs aren't the best option right now. Freerolls are always a good way to practice, though.
2.) I believe this depends on the format. In cash games, a HUD can really come in handy, assuming that you know how to use one properly, but in SNGs and tournaments, I don't think it matters all that much.
3.) If you choose cash games, I recommend taking a look at the Overview of No Limit Hold'em lessons. There's a similar overview for SNGs, and also a quick beginner's article to get you started right away. There's also a free tool available for download here called the ICM Trainer, which, while it's a bit rusty nowadays, allows you practice those decisive Push-or-Fold situations in SNGs. Just keep in mind that you're not allowed to keep it running while Pokerstars is open.
And if need be, you can always brush up on your Poker basics with these articles, some which are already included in the NL Hold'em overview mentioned earlier.
Oh, and one more thing: If you don't have an account at PokerStars already and plan to open one for this, be sure to sign up through PokerStrategy to get access to a tracked account, allowing you to unlock more content just by playing. Check out some of the offers over here, you might even be able to boost your starting bankroll that way.