iPhone 6 memory issue!!!!!!

Try doing a full restore and set up as a new device. If you restore from backup and keep having the same issue, you may be restoring an issue back to the iPhone.

YOu could transfer the photos to a computer first.

YOu could use icloud for the contacts. There is also an app in the app store called My Contacts Backup.

You should be syncing your contacts to a supported application on the computer or to a cloud service. If the only backup you have of your contacts is in iTunes, you are just waiting for problems. You should have everything synced and backed up so that if something was to happen to your phone, you could recover all of your data. With the couple of comments that you have made regarding photos and contacts, you are just flirting with failure, because it will happen. Photos are designed to be imported to the computer like any digital camera. Then you can use iTunes to sync them back to the phone. If you are not backing them up by importing them, and you are just relying on the iTunes backup, again, you will lose them. They are only residing on the phone. Bad idea. Even the support documents from Apple regarding backups recommends you not rely on iTunes as your only backup for contacts and calendar, since the iTunes backup can fail or become corrupt, which is what sounds like part of your issue is.

• Use the directions on this link to redownload your previous purchases: https://support.apple.com/en-us/HT201272
• this link shows how to set up iCloud: https://www.apple.com/icloud/setup/ios.html you turn on contacts when you set up.
• this link also explains how to get your contacts back from iCloud: http://www.imore.com/how-restore-contacts-icloud-your-iphone-or-ipad

I have the same issue... my iphone 6 displays a small amount of free memory compared to what iTunes shows when the phone is connected to the computer...