How do my camera roll backups and shares work?

When I backup my camera roll from my phone, 

1) Do the photos remain on my phone?

The photos will be on both your camera roll and your Amber X.

2) If I delete a photo from my phone, what happens to the backed up copy on Amber X?

If you delete a photo from your phone, the backed-up copy will remain on your Amber X (your private Home > My Devices > this device).

3) If I delete a backed up photo on Amber X, what happens to the original on my phone?

If you delete a backed-up photo from your Amber X, the original photo on your phone will remain and it will be backed up again when you toggle the automatic backup.

4) These same questions apply to files that I might be syncing between devices, how does that process work?

Currently, only camera roll is allowed to be backed up from your mobile phone on the mobile Amber iX app.

5) Also, if I create a "public" link to share, can I delete/decommission that link later so it can no longer be used? 

If you delete an item that was used in a share/public link, then that share will be invalid.