Perhaps more rare in the surface Navy than subs? I regularly heard of them being awarded to firing units. (post 9-11 timeframe)
Of course I have been wrong before on more than one occasion. I'm probably confusing them with Battle Es.
Unlikely. From Wikipedia: The Presidential Unit Citation (PUC), originally called the Distinguished Unit Citation, is awarded to units of the United States Armed Forces, and those of allied countries, for extraordinary heroism in action against an armed enemy on or after 7 December 1941.