Game Center under different Apple ID than App Store/iTunes?

This question possibly comes to my incompetence in regards to technology, as I'm just afraid to mess things up if I fiddle with them. Then I'd have the issue of returning them back to the way they were, which would be incredibly tedious and frustrating. In short, my iCloud email is registered as my Apple ID for my Game Center account, while my App Store and iTunes are both set up under my dad's iTunes account. I would like to change this, but am afraid that if I do, it will delete all of the progress I've made on my games.

In case this isn't clear enough, I'll give a long explanation to clarify what I mean, so that I can hopefully get a solution beyond "no, you cannot resign an account to an Apple ID", in which case I'd be stuck. When I first got my Ipad Mini as a present from my parents a few years ago, my dad set up my Apple ID under his iTunes account. This meant every time I downloaded an app from the App Store, it was a purchase made from his account. So, as I got older, I had to give him the money for any songs or paid apps I wanted to purchase, which grew old quite fast as we live in different city's and as I stated earlier, I am not skilled with technology. At the time, however, he did not set up a Game Center account. When I began downloading games such as DragonVale, I decided to log in to the Game Center so I could friend other players and trade Gems and whatnot. So, I signed on using my iCloud email, which is my own and not my fathers. Now, I would like to make my own iTunes account with my own money to be more independent of my parents. There's a slight problem with that.

When you go into "Settings" on the iPad Mini, and then go under "Game Center", the first thing it tells you is the Apple ID it's registered under. Apparently, my Game Center account is under my iCloud email, listed as my Apple ID. That confused me, as I found that my iCloud email was in fact not my apple id- correct me if I'm wrong. If it is, and I can connect it to my bank account and use it to purchase songs and apps, that would be great. Everything else on my iPad, iTunes and the App Store, are connected to my dad's iTunes account. I read numerous times that once an app is downloaded under a specific account this cannot be changed. However, at the very least I would like to know; if I change my Game Center's Apple ID, will this delete my app's progress? And, since the other answers which I read were confusing: is there a way I can change my iTunes, Game Center, and App Store ID/account without deleting music/songs/pre-installed apps & game progress? Thanks in advance, and sorry for the long post and reiteration