For the Festival of the Lion King and Beauty and the Beast shows, 20 mins is more than enough. We usually show up about 5 -10 min. before these shows and have no problem getting seats. If you feel really strongly about sitting in the front row at the shows, then you'll want to arrive earlier.
I'm not a fan of Fantasmic, so I won't go to the theater more than 15 min. early if for some reason we decide to see it. Haven't had a problem getting a seat doing that. However, we usually are sitting in one of last two sections of the theater. That said, I don't think you need to be at the theater by 7:30. I think 8:00 should suffice for a good seat. However, I'm sure someone who is more of a fan of the than I will be along with more tried and true advice than I have on that one.
JTA- wish I advice based on experience, but my DD wasn't interested until she was too old to do it. I've seen some good advice on here about having one adult go sign up the kids at 9:00 while the other remains behind. Also asking for your check an paying it at the beginning of the meal so you get up and out. Character meals take anywhere from 60-90 mins. depending on your group and how fast the characters make the rounds.
I notice the end of your trip coincides with the start of Star Wars Weekends. If you were planning to do JTA on May 17 or 18, I believe you have to have the kids with you to sign them up. (I don't think that is the case on non-SWW, but can't remember for sure) There will also be a huge rush to sign kids up for JTA at park opening. More so than on a normal day. So, being out of your character meal and on the way to the sign up location at park open is imperative. The slots fill very quickly during SWW.