1) Which you use should be based on how far along you are in the game and if you have decay rate amulets. Early game, if you have an amulet, your focus should be on your main stat. Trying to maintain a 1.50x multiplier means using your weak secondary appeal and costs you points. It's better at that point to hit 1.50x and just use your main until a burst. Actually, if you have an amulet, you probably just shouldn't burst at all since bursting early game costs you points, too.
If you don't have an amulet, it's trickier. I guess you can try to maintain your multiplier, but that's not easy to do. Honestly, for your first game, through, I'd recommend balancing all stats and picking up the three decay rate amulets. This minimizes point loss until you can focus on two stats, which you should do from every game after that. If you're balancing all three, just appeal in order. I wouldn't bother bursting for a while.
I can't really remember when bursting becomes useful. Maybe around the halfway point (after the second forced festival)?
2) As stated, it's for amulets. I wouldn't bother with these until the second half, when your schedule tends to be a lot more open since you don't have lessons to worry about. You'll probably be running a lot of performances for money at that point anyway, so just look out for the ones that have the amulets you need. (You'll want the three decay rate amulets and at least one of the two voltage increasing amulets, if not both.)
3) I'm not sure if it is, but if it's an issue of treatment, do your best to spread your focus. Honestly, I've had zero trouble even when I make my main idol do jobs before anyone else and always pick them for janken at night when given the option. The key is in the morning communications. Always make the two support idols happy (which means always picking your main idol), even if it means ticking off your main idol. Even if you only focus on them indirectly in the morning, their affection will eventually be high enough for them to start participating in the nightly conversations before they leave.