SFF 1. My first ever tri was in appalling weather done in the south. I used an IKEA blue bag, just put it on its side and made sure that my shoes were holding it down it was that bad. When I came out of the pool it took a second to move the shoes and pull out a top to put on, number etc. Some races do not like crates as they take up too much space.
2. Just be more careful, try a practise ride in the rain if you can just so you have an idea how the bike will handle.
3. Goggles essential, I like zoggs but the fit is essential. If you hold them up to the eyes and press them in place without the straps they should stay for a few seconds proving a good fit. I also use a nose clip.
Definitely works looking away and down, the dog will wonder what you are looking at. Just coop going is correct keeping arms still and by your sides, I find that my slow speed is not much of a threat to them.