Hey! I think it's GREAT to have so many character meals! It really adds to the experience with your children. I'm assuming you're asking what to do at the character meals and not out in the parks so I'll go that route....
First, at MOST (I really can't think of one you don't) character meals you simply wait for them to come to your table...they have a natural "flow" going from table to table and when kids come running up that take them off the flow it's so sad to see that table that has been anxiously awaiting their child's first Mickey hug to have him be delayed another 15-20 minutes...they're pretty good about getting back on track and will wave to those that run up sometimes telling them they'll be right there....I would have your autograph book ready for them to sign and as far as I can recall only the people characters talk...so you can ask Goofy and the rest questions, you'll get some pretty funny body language responses!

I think the characters do a great job at asking YOUR children all the good questions, it makes your kids feel special and for the non-speaking characters they can really ham it up...my son's favorite was Goofy who (at Liberty Tavern) kept sneaking up behind him and making faces without my son knowing, then every time my son would go for a fork of meat or mac/cheese Goofy would take the spoon and fill it up with veggies..making him eat those first...if my son tried to eat the roll or something else, Goofy would put his big hand over the front of his face to keep him from eating...just really funny stuff. I would just say enjoy the experience the first few times and on your 4th or 5th start asking questions, I think for children if you give them questions (I'm assuming you've got children

) to ask they'll be too nervous when they actually see them they might get frustrated trying to remember what they were supposed to ask and lose the joy of the moment....just enjoy and hopefully others can share their experiences and any fun things they did to make it more...my kids loved the autograph and always having the camera ready for pics...we have 3 kids so with the 'speed' the characters have to move through, a pic and autograph and a small chit chat is a lot for our table!
Enjoy!
Tara
I will add that it's part of the magic to say things like "Cinderella, it is so nice of you to have our family at your castle, it's lovely" or "Chef Mickey, Dinner was amazing...our family is so excited to try out all your dishes!"...