I'd see if I could get a road bike - if budget a problem, then 2nd hand will get you far more bang for buck. You could put slick tyres on your mountain bike & get a track pump to pump tyres up really hard, but you may well be able to pick up a very old road bike for not much more.
Swimming - just get on and do it. A coach will help. It is possible to swim breaststroke, and some of the time lost is offset by the fact that you can see where you are going and will probably swim straighter. The way I did it was to start to putting one length of crawl out of every 4 breaststroke. I then gradually went down to alternating, then 3 crawl, one breast, and eventually just though sod it and swam the whole session fc. I now find fc is by far the easieast & breast much more tiring.
Timings I wouldn't bother about too much. As has been said, just concentrate on getting round, but I'd also add make sure you enjoy it!
Make sure you do some brick sessions in training (bike then run) because at first it feels like you are suddenly 90 years old when you try to run after the bike.
Don't expect your run time to be as fast - I did 52 mins in my last tri, when I would have expected to do a straight 10k in about 43-44 mins. Not one person in the race did the 10k in under 40 mins!