... then quits and app doesn't start, removed preferences but still same result, run xattr -cr application.app but no result, gatekeeper knows I want to open it but still no results, any suggestion?
Hmm. And everything is alright with app-related items in ~/Application Support; /Application Support; /LaunchAgents; /LaunchDeamons; ~/LaunchAgents ?
You can try with a Safe Mode
Or try copying the app to ~/Applications and run it from there
Sure thing, you can put a copy of the app into .dmg archive to run separately. or download dmg version of that app