iCloud system iPhone 3G

Okay, hi guys.

Picture this:

1          There are 2 Apple IDs, A and B. Apple ID A is my mother's, and B is mine.

2          The iPhone is my mother's, so naturally she would sign in her account on anything that she does on the phone.

3          Now, I have played some games on my mother's phone (and of course, unlocked some game progress).

4          Can I transfer the save data (or game progress) to my Apple ID account? (through iCloud?)

Now,

5a               My mother signs in her ID at the App store, iCloud and Game Center. If I have played some games on her account and unlocked some game progress, can I just sign her out of everything and log in to my ID, and from there, take the necessary steps to save my progress?

5b               When syncing with a computer (that has been synced before with Apple ID A), will the computer detect a mismatch of ID (because I am syncing for B) and attempt to "delete the data"?

If everything is successful (which the point in asking this is to know whether the thing that I am doing can be done...)

6                 Take it that all has been successfully done. If let's say I have saved progress in a game and I have successfully saved that onto iCloud, then is it correct to say that if I delete the app (but keep the data), then some time later if I redownload the app again will my saved progress be there?