Is there a way to quickly view which heists I have done and on which difficulties?
This answer assumes you're playing this via PC and Steam.
In the FBI Files (fbi.overkillsoftware.com, or accessible in-game from the main menu), you can check which heists you've completed by looking at your own profile and clicking the "view suspect's statistics" button.
Another way to check which heists you've completed is to check your achievements. This is however not as good as the FBI files, as the FBI files shows what you've completed in an easier to read format.
Do note both of these ways only show if you've beaten heists on Mayhem difficulty or above.