1. Settings>iCloud and scroll to the bottom. In your iOS version, the option is listed as "Delete Account"
2. Unless you use a separate email address for iTunes & App Store purchases, they are one and the same. Signing in with your Apple ID into iCloud adds the iCloud Services to your Apple ID.
3. 5 GB is given to you for free with your iCloud ID. (You can sign up for 50GB storage for .99¢/month. This is monthly and can be cancelled or changed anytime)
4. You and your father can share the additional storage space that he has signed up for. Your backups will remain separate from one another. The fault of this is that you will have to always keep Contacts, Calendar, Reminders, Safari, Notes, Keychain, Photos, and potentially Documents & Data toggled off on your device, or risk sharing/merging these contents with one another. If you share them, if one of you deletes anything related to these sync services, it will be deleted for both of you. (This is why it is recommended to use your own account for iCloud especially)
Note: iMessage and Facetime - You should also check these settings to make sure you are not signed in with your fathers account or you could run the risk of sharing your text messages and FaceTime calls.
Should you upgrade your iPhone to a newer model, you will be at risk of sharing even more like actual phone calls.
Use Continuity to connect your iPhone, iPad, iPod touch, and Mac - Apple Support