You can start with gentle excersises straight away (the middies were telling me to start excersising pelvic floor and ab muscles on day 2). I am not fit at all, but I would think you can resume doing whatever as soon as you feel ready, after a VB. If you have a C/S it will likely be a different story.
One thing to be mindful of is whether heavy excersise will affect your milk production - I think with SOME women it does, though I'm not sure how common that is.
How long it takes you to get back in shape is totally individual. I could be wrong, but I would've thought if you were careful about putting on weight and kept up some level of fitness (whatever you could healthily manage) during your pg, you should be able to get back to normal quicker afterwards. Of course, as Nadine said, you may never go back to the way you were... But hey, you'll have a new little baby and so your life is changed permenantly (for the better of course!) anyway
About the plane thing, I'm not aware of an age limit generally speaking. It may depend on the particular airline's policy?
Re the theme park - do you have a sling or carrier? They are wonderful for taking a newborn out and about. It is up to you as to how comfortable you will be in that sort of environment though - it took me a while to get my head around having a baby and I don't think I would've been psychologically ready for a theme park until DD was a good few months old! But that's obviously a personal thing, and everyone's different.