I expect the natural answer is EDT (Washington DC time) but it's an extremely legitimate question in a country as big as the US and it should have been stated more clearly by the Dyslexic In Chief.
Mea culpa. Makes sense when someone can't distinguish between themselves, their business and a country, so it would never be UTC. That would be too convenient for other people.
Midnight never refers to 11.59pm, which is one minute before midnight. I can say that for certain.
Normally I would take "midnight on Friday" as an instant to mean 2400, since if you're somewhere at 1am on Saturday morning you wouldn't consider it a problem to say "we were out partying on Friday night", but if you were there at 11pm on Friday night you would consider it a problem to say "we were out partying on Saturday night.
However in the particular case of something beginning, I would normally take take it to mean "the very start of Friday according to legal time".
Likewise, in the particular case of something ending, I would normally take it to mean "the very end of Friday according to legal time".
Dutch media reports "night from Friday to Saturday", so it's the latter. But that still leaves the open question in which timezone the 11:59 is in (and whether that's a static timezone, or based on local time at departure/arrival), and whether the 11:59 refers to actual or planned time of departure/arrival.
Yes, multiple news media reports the ban going into effect on 11:59 pm Friday. Some (e.g., "The Sun") report it as 12:00 am Friday. Unless they give an official answer from the White House, I would not consider either report from news as reliable. "Midnight Friday" can be interpreted both ways until they clarify.