Q: How do I restore my I cloud if I already set my new phone up as a new phone

See the instructions below from Transfer content from an iPhone, iPad, or iPod touch to a new device - Apple Support

To transfer a backup to a device you've already set up, you need to erase the device: Tap Settings > General > Reset > Erase All Content and Settings. This will erase any data that's currently on your device. After you've erased it, your device will restart and you'll see the "Hello" screen. Now you can transfer a backup to your device.

Yes -- as stated in my reply above. You did the right thing by installing the most recent update (9.2) and that update will not be erased when you follow the directions. However anything else you may have added to the new phone will be erased.

Yes, but you are restoring a backup. So you will end up with whatever the content of that backup was.

You will have to reload the music again, unfortunately. However, if you are doing it by manually managing your music switch to syncing by unchecking "Manually manage..." Then, with the phone connected, Click on the phone's icon, then the Music entry in the list on the left. Select all of the music you want (or all music), and click Sync. It will run unattended after that. So it will still take hours, but not your time.