Delete all data on exit
Is it possible, as it is in firefox, to delete all data when exiting a session: cookies, visited history, data stored by sites, search history, etc.?
Not yet. You can set this per-website under site settings as seen when you click on the icon at the far left of the address bar, but you can not set it for the whole browser as yet.
You could just use Private Window(s) for your browsing.