1) In tempo is fine. Tempo doesn't HAVE to be super quick, though it should be as consistent as you can make it. What's "acceptable tempo" varies some by the situation -- if the auction goes 1S-2H-4S to you it's expected you'll take a little longer to act than after three passes. Note that
thinking is never ever an offense, you sometimes get complicated decisions and need to work through them -- taking advantage of partner's thinking to infer what he has is the problem. It's actually recommended that declarer take a bit of time before playing to trick one -- you should want to do this as declarer, and it's also courteous to the defenders. I don't know that 30 seconds is necessary unless you're in a high level game, and sometimes a hand is just super obvious and you can just play. I tend to play very quickly though.
2) Some of each. Beware that some BBO randos are paragons of Dunning-Kruger and think they know what they're doing. Robots aren't very good (and for instance don't signal on defense).
3) For beginners who aren't sure about bidding and basic card play, I'd recommend
http://www.kwbridge.com/ as a free, super basic resource. There are a lot of different books out there that I might recommend depending on what you're curious about.
4) There are times when it definitely does matter, notably when deciding whether to save over an opposing game or slam -- knowing about what that's worth, and what your save might cost, is vital. Down three doubled against a game might be good, or it might be very very bad, depending on vulnerability. Having a sense of that is vital, and while I don't know that 'memorizing' the table matters, being able to calculate it is a good idea. That's not too hard.
5) I personally count down from the missing cards, but both ways are acceptable. Do whatever's easier. To start, count important suits (trumps, and suits that you plan to run or score long cards in). There's a fun little "flash card" type game somewhere that I can't find online that's nice in terms of establishing hand patterns -- which is even better than counting. You've got X, dummy had Y, and as soon as someone shows out they had Z, which leaves # for the fourth player. If you play enough bridge those numbers become second nature.
6) I'm certainly willing; evenings US time are best. Post 1 of the thread contains a bunch of BBO nicknames including mine. PM me here if you want to discuss setting something up.