Beginnertriathlete.com is an excellent resource to answer all of your triathlon questions. I'd
highly recommend checking it out.
In response to your questions:
1. To paraphrase the former Sec. of Defense, you do the best you can with what you're given. If a 10 meter pool is all you have access to, use it. Again, on BT.com, there sould be training plans/tips conducive to working out in a smaller pool.
2. What you're doing is a sprint tri, and is a perfect starting point for a beginner.
3. You can wear whatever you feel comfortable working out in. I did my first duathlon in gym shorts and a cotton T-shirt. Problem is, a duathlon doesn't have a swim, so that's where the clothing question may get a bit dicey. I know there's several posts on BT.com for appropriate attire. (I'm assuming that, since this is your first one, you probably won't want to invest a lot of $$$ in tri-specific clothing, until you're sure it's going to be something you want to do again. BT.com should be able to direct you to pretty good deals.)
4. A mountain bike should be fine. In most of the du's and tri's I've seen, there's a varied level of fitness amongst the competitors and cost of equipment. Don't be afraid or nervous...everybody else there had a starting point as well.
But again, there's multiple tri specific websites, and BT.com is amongst the best. There's also loads of books on the market. Good luck!