Q: iPhone restore problems

Hello Husar117,

Thanks for that info and choosing the Apple Support Communities. I know how important getting your apps and music back on your replacement iPhone is to you! Based on what you stated, you may have to do a manual sync of your music from iTunes to your iPhone, as music is not contained in an iTunes or iCloud backup. 

Sync your iPhone, iPad, or iPod touch with iTunes on your computer using USB

Here is more on what info is kept in backups:

About backups for iOS devices

Also, you mentioned that there were a couple of apps that you were not able to be restored. If the app developer no longer offers the app, that would explain why this happened to you. Good news is you can still manually sync this app to your iPhone if you have a copy in your iTunes library on a computer. This article explains more about accessing your past purchases:

Download your past purchases

Cheers!