1) Almost equally important (as outlined by deano)
2) I'm pretty sure strategy only comes into play if "you" have been ejected. The bench coach's other ratings (hitting, pitching, fielding, etc.) can help (or hinder?) player development at their respective level, but I also believe that this effect is more pronounced in the minors.
3/4) I agree with all that deano has said, but I'll add some more. Of course, a SP with 75+ control and splits with 80/70/60/50 is going to be pretty good, but those guys are also somewhat uncommon (and thus, expensive). Finding undervalued pitchers is one of the most fun parts of the game, and goes a long way toward your success. I'm usually more willing to take a risk on a guy with splits in the 60s if he's got two pitches and control over 75, especially if his velocity is 50 or above. (Velocity sort of helps pitches become a little better, it seems to me.) This can be especially effective in pitchers' parks. But I have seen very effective pitchers with 80+ splits and no pitches above 70, but they aren't going to strike out too many guys and will put up a stinker of a season if you give them enough time. As long as a pitcher (starter or reliever) has two quality pitches and ML-caliber splits and control (generally considered to be 60 or above), he can probably be useful. A starter is going to need a third pitch of some sort, but I don't worry too much about how good those are. I try to stay away from RP with only one ML pitch and a second one below 70; others have success with them, but they make me nervous. I also don't like the guys with a second pitch better than their first one, but that's just a prejudice on my part.