J.--Good morning! I don't know how to stop your daughter's fears but I do think she may be getting more exposure to events that could be fanning them than you realize. There has been a lot of news coverage on Tornados, hurricanes, tsunamis, etc. My guess would be that she is seeing these images (even if it is just in news breaks or commercials) and is being frightened by what she is seeing and hearing. If I were her age and heard about Tornados wiping out an entire town or that hundreds of people drowned in a flood of some sort I would start to worry that it could happen to me also. I would try talking to her about why the storms scare her, what does she think may happen? And then if you haven't--make a safety plan together---or go over the one you have and that may help her feel more comfortable with the storms. As far as the water issue, I again would ask what does she think will happen? If she is ok jumping off the stairs is there a reason she has to jump from the side or are you just trying to prove that it is ok? If it is not part of the lesson that she jumps from a particular spot I would just let her jump from were she is comfortable. As long as she learns what to do once she is in the water I think she should be ok ---and she may just grow out of this on her own as she starts to interact with other kids her age at the pool and they are jumping in and playing games.
If the fears start to get worse you can talk to your pediatrician and see if he/she can recommend a professional for your daughter to talk to.
Good luck