Q: Can I switch my AppleID?

Anything purchased with the Apple ID that you share with your dad will need to be purchased again on your own Apple ID. Once you have your own Apple ID, do this: Sign in with a different Apple ID on your iPhone, iPad, or iPod touch - Apple Support

You can create your own Apple ID at: http://appleid.apple.com as long as you are 13 years old or older.

When creating your Apple ID you may find this useful:

Create an iTunes Store, App Store, or iBooks Store account without a credit card or other payment method - Apple Suppor…

You can then sign out of your Dad's ID in Settings->iTunes & App Stores->Apple ID on your iPhone, and sign in with yours.

All content purchased with your Dad's ID will remain tied to it, and apps will still require it to update.

Anything purchased with the Apple ID that you share with your dad will need to be purchased again on your own Apple ID.

Not really. All purchases will remain on the iPhone and continue to be usable. In the case of Apps, the original Apple ID and password will be required to update.