The biggest safety improvement the NFL could make by far would be to remove helmets. While this sounds paradoxical, helmets allow the kind of plays which result in concussions. Remove them (and obviously forbid any tackles above the chest area) and you'd have a much safer game; see for instance, this article from The Guardian.
The chance of this happening is ...
The practice gained major visibility in UEFA competition when Marcelo Brozovic slid down behind the wall on a Suarez free kick in 2018. Lionel Messi was actually there, but it was Suarez taking the free kick, not Messi.
However, it was in Brazil that the practice came into being. ESPN has a nice article about it; the takeaway is that the practice of ...
Yes, it counts - in general, penalties during regular play are not treated any differently from other goals in in football.
Disclaimer: A "shutout" is not something defined in the Laws of the Game (even in the glossary), so for a definitive answer you would need to refer to whichever organisation is collating the shutout statistics.
I'm not sure it's that true that EPL grounds are that much smaller than European grounds, at least for the "Big Six" (and Wembley):
City of Manchester Stadium
For non international matches, the pitch size can vary quiet a bit. The pitch has to be a rectangle whose width can be anywhere from 45 to 90 meters, while the length can be anywhere from 90 to 120 meters. So a football pitch can almost be a square!
However, the international pitch dimensions are much stricter. The width has to be from 64 to 75 meters and ...
The pitch most definitely varies in size, but not terribly much. See this page from the BBC for example. England's rules are very wide - the pitch must be between 90m and 120m long, and between 50m and 100m wide (!!) - that's a big variety, though - but for major (or even mid-level) play, it's pretty close to standardized.
This page lists various Premiere ...