No, not possible unless your files were on a removable SD card. Should not be too much to fix the port though, especially if you really want those picture. Keep backups next time, either copy to a computer or store in cloud storage. Google Photos automatically backs up your files so you don't have to worry about losing them
Yes as the previous answer says repair the port of the phone. It is really cheap.
That happend to me too; but my phone had a removable back, so I swapped in my spare battery, quickly backed up and reapired
The S6 Edge doesn't has removable back, so only option is to repair port.