Hi NickNotorious,
Thanks for posting your question in the Apple Support Communities! I understand that you have some questions about restoring content to your iPhone after having a repair done. I definitely wouldn't want to lose any information, including my photos so I can understand wanting to make sure you get everything back on to your iPhone. I'm happy to provide some direction here.
To answer your first question, iTunes can keep multiple backups. You can use this link to help you locate your backups.
Locate backups of your iPhone, iPad, and iPod touch
If you're looking to restore your photos from an earlier backup, you'd need to restore that backup to the iPhone, then import the pictures to your computer. An exception to this would be if you're using iCloud Photo Library which will automatically sync your photos from your iPhone to iCloud which can then be synced to your computer. You can find info for restoring a backup, importing photos, and iCloud Photo Library in the resources below.
Restore your iPhone, iPad, or iPod touch from a backup
Import photos and videos from your iPhone, iPad, or iPod touch
iCloud Photo Library
To answer your second question, in order to restore your text messages, you'd need to restore the entire backup. You aren't able to pick only certain items to restore. Based on what you've stated, your best bet would be to restore the backup with the photos, import them to the computer so they are saved, then restore the most recent backup so that you have the most up to date messages.
To address the issue with the automatic sync, you can take a look at the information here to disable that. I've included the information for both Mac and Windows. You'll want to check step 5 for how to make sure that the automatic sync is disabled.
iTunes 12 for Mac: Sync iPod, iPhone, or iPad
iTunes 12 for Windows: Sync iPod, iPhone, or iPad
Take care!