In this (bankroll, BB/hour, etc) context BB is a Big Bet. At a $1/$2 table the Big Bet is $2.
300x BB (Big Bet) in a $1/$2 game = $600 (or 6 buyins). That seems to be standard. Again, this is highly dependent on whether you have more money somewhere if you run out.
I would not say it is EASY to loose a buyin at $1/$2 but it is possible. Depends on the site (quality of players, table selection possibilities, etc). I don't think waiting till you are down half your bankroll is a good idea. Before you are out that first $100 you should have a pretty good idea if you are being outplayed, just getting bad cards, or both. I would not suggest buying in again without looking over your hand histories and trying to figure out what you did wrong. You would likely be playing scared not wanting to repeat the loss and even the next day, I would think it hard to play your best game having lost 1/3 your bankroll the day before.
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