does itunes overwrite previous backups when starting a new backup

I realize it's too late now, but for the future in iTunes go to Preferences, Devices tab, and check the box to disable automatic syncing.

If you kept a parallel backup in iCloud you can still restore from that.

If you have regular backups of your computer you can restore a previous iPhone backup from the computer backup.

I don't understand what this means. Also, do backups of a previous version of iOS get automatically overwritten once you upgrade the iOS of a device and do a backup? Because I helped someone do a backup in iOS 8, then we updated the same phone to 9.3.5 and then did another backup. The only backup visible in preferences was the new 9.3.5 one. Is that how it's supposed to work?

iTunes only keeps one normal backup per iOS device, and yes, it is an incremental backup in that only data that has changed is backed up or deleted.

I should add, if you have space available, iCloud will keep three normal backups per iOS device, unlike iTunes.

Good to know that. I just learned something.

Well, you most likely pay for the storage, you only get 5GB's free.

Actually, there is a way to archive your backups in iTunes and then you can restore them:

http://appletoolbox.com/2013/08/how-to-restore-ios-devices-from-older-archived-i tunes-backups/