Do you want to send all messages to her phone? It's easy to export your messages to excel document as a backup or send it to someone, all data sort by following format:
Name PhoneNumber Datetime Type(send/received) Text
I think it's nothing to wrong about, I used to use Android device and usually got system stuck or random restart problems. But everything seems ok after I restart the device. I also have similar problems such as screen stuck when I use Facebook or YouTube in iPhone 7 (iOS 10.2), my friends and...
iTunes is very disgusting that you can only restore with the whole backup. It seems you need to "extract" data from the backup, there are multiple 3rd party software could do that, you can get the data to your iPhone or computer, it depends on you.