How can I stop this - can i delete all of this?
You could. Just be sure that you have at least one backup of your disk, and that you are comfortable with doing a complete restore if something goes wrong.
I assume you plan to not use adobe software anytime soon.
If I were you I'd not worry about all these small files associated w/adobe software. They will not hurt your mac in any way, and most likely are taking up 0.0001% of disk space. I'd be more keen to get rid of adobe
software that is running in the background and is launched at startup. Look for anything adobe in /System/Library/LaunchDeamons, /System/Library/LaunchAgents, and Users/username/Library/LaunchAgents, place them in trash and do a restart. You could check with Activity Monitor for adobe processes running before the restart, and check that they're not running after restart.
That would do it for me. I've done it before. Don't worry about those little files left behind. There are applications that claim to be able to identify files associated with a certain app, and remove them, but I never used them. Because; how can I trust them not remove something I don't want removed; and why should I risk it if it's not necessary?