Ah the good ole tampon question.
Well, first of all, make sure you insert it right and, while feeling really strange at first, you shouldn't feel it in you at all after you insert it. As for taking it out, it doesn't hurt--you just need to make sure you're relaxed and that your muscles aren't tense both when you insert the tampon and when you take it out.
As for the theme park question, the first time I ever went to an amusement park I had to wear a tampon! Nothing dastardly happened (even though I expected it, I'm just as period paranoid as you probably are)--you just have to make sure you change it a lot (which can be a bit of a nuisance) but make sure you change it before every four hours--I know the box says change it every four hours but you can still leak a little bit and by changing your tampon maybe every two hours can help with that.
Tampons can feel really strange at first but you don't feel like you're wearing a diaper and you really can carry on with routine events without the feeling of paranoia
Hope that helped and hope you have fun!