It takes at least a day to do SW if you want to see everything. We spent a full day plus 2 half days there in Feb. We did see some of the shows twice, but there was a lot that we didn't see the first day and did later in the week.
Not sure about the rain-but I wouldn't see why not. After all Discovery Cove is open in the rain, and you're not swimming at SW. Most of the show areas have a cover over the seats too, so while you're outside, you're not completely exposed.