Welcome Back Lisa!
I am a big fan of
Characters-in-Flight at
Downtown Disney and consider myself a frequent flyer.
This is a great question and one I wish I had personally known the answer to a couple of years ago when I was at Downtown Disney with one of my friends. We both wanted to do Characters in Flight but it was very windy. They told us to check back so we ate and came back. They still weren't flying so we went shopping and came back without success. We walked a lot and knowing a number to contact them would have been a lot easier.
The direct number to the ticket window next to the loading platform at Characters in Flight is 407-938-9433. They have a pilot there who watches their Doppler Radar. If they aren't flying at the moment, they can give you a prediction of if and when they will be flying that day. If you are a part of the twitterverse, you can follow Characters in Flight @DisneyBalloon. They sometimes tweet updates but their direct number is likely your best bet.
Tickets are not sold in advanced but may be purchased at the attraction's ticket window. They don't sell advanced tickets because as you said, weather is a huge factor in determining whether or not this attraction will be operating. Weather conditions also determine the number of Guests who may board the gondola on any given flight. I think there are too many variables to sell advanced tickets.
Weather permitting, the hours of operation are every day from 10 a.m. to midnight.
Please feel free to visit with any other questions. Its our pleasure to assist you!
Wishing you minnie magical memories :-)