On an Iphone 6, can I recover deleted text messages?

Yes, if you have a backup.

Retrieving isn't as easy as you think it is...

Restoring from iTunes backup is an option but you need to restore the entire iPhone (only messages restoration option does not exist) including all apps, Photos, Videos, Voice Memos, Notes on your iPhone etc...

The question is when did you backup on iTunes and when did you delete it...Read on...

Let us assume...

Date1: Backup date

Date2: Message Deletion Date

Date3: Current Date / Restoration Date

Given that --> Date1 < Date2 < Date3 

1. Risk of restoring on Date3:
   1. You may lose data between the Date1 & Date 3
   2. By default, iTunes creates incremental backup over the existing backup such that you only will have one backup per device on iTunes
   3. If you have taken another backup between Date2 and Date3, then the messages that had been deleted on the device on Date 2 is also deleted on the backup.
   4. If point no. 3 is true the messages or lost completely.
2. Else you have a mitigation process: Create Multiple back-ups on iTunes for the same device.

How to create Multiple Backups for the same device.

1. On iTunes Click on Manage Backups
2. Right Click on a Backup and Click Archive
3. Click Backup Now.
4. You will see a fresh backup will get created See the GIF below

1. Restore from Backup dated Date1 (Archived)
2. Retrieve the message and store it separately
3. Restore from Current Backup Date3

No

No, you need a phone that can run iOS 16. That would be an iPhone 8 or higher.

Trying to restore from a backup of the iPhone would not be practical since the next backup after the text deletion would pick up that action and the text would be deleted from the backup.