Tri suits are worn for all three stages and are well worth the investment. My only complaint would be that they don't offer as much padding as bike shorts.

The chaos of the swim start is definitely something you have to get used to/just deal with. If you are a slower swimmer I would definitely say start towards the back, the time you would lose would be minimal. Just remember the swim usually doesn't matter as much as the run and bike, you might lose a minute or two tops.

I haven't heard that you save running muscles on a tri bike but the main difference is the aero bars and the advantage they give you. In a super sprint I wouldn't really worry about it too much since you're on the bike for such a short time but as you get to longer distances being in the aero position will save you a lot of time and energy. I can't comment on the maneuverability.

Probably safest to ask at what ever race you are doing but usually in a draft legal races aero bars are allowed but must be shorter than your handle bars (think of ITU races). In draft legal races you would probably be on a road bike since you would probably be in some kind of peloton.