Screenrant answered it pretty well:
Earth 89: Tim Burton's Batman Movies
Tim Burton's Batman films are represented in one quick cameo, which confirmed it as Earth-89. Danny Elfman's familiar Batman theme plays as the Bat-Signal burns bright in the red skies over Gotham City. This is observed by a man in a trench-coat and fedora, who mutters "I hope ...
You are missing out few, will try to answer in chronology:
From Supergirl S05E08:
Tim Burton's Batman Movies: Alexander Knox (Robert Wuhl) cameo who was the first to report upon The Joker's crimes
Titans: Hawk (Alan Ritchson) and Jason Todd (Curran Walters) cameo
Batman (1966 TV series): Robin (Burt Ward) shouts "Holy Crimson Skies Of Death!"
From Crisis: Episode 2 (Batwoman)
Legends of Tomorrow have retired and Mick Rory is left inhabiting the Waverider
Batman (Kevin Conroy) has retired and can only move thanks to an exoskeleton.
Superman of this Earth is killed by Lex Luthor wielding the Book of Destiny
Superman (Tom Welling) has given up his ...
First thing first there is no Crisis on Infinite Earths S01E01? As it's not a different show but a crossover of five existing Arrowverse showa with some extra additions.
First Crisis on Infinite Earths is not limited to The Flash and Batwoman and if you don't know other shows you might end up getting confused. Also, Crisis on Infinite Earths is 5 episodes (...
Brad Hunter (Comics - appears in 1 issue)
Lacy Warfield (Donnerverse - Superman IV: The Quest for Peace
Mark Spencer (Comics - appears in 6 issues)
Jeff Hage (Comics - 9 issues)
Jennifer Owens (Comics - 13 issues)
Franklin Stern (Comics - 33 issues)
I am up to date with only Flash and Arrow
You should be fine.
To date only Flash and Arrow have had the Crisis as a plot point, the other shows have not featured any elements of the proposed crossover although characters from other shows are expected to feature in the crossover episodes.
At best, the pre-crossover episodes of other CW /DC shows have only ...
They have never been in the same continuity.
Most people assume that they share the same continuity, and particularly that the Doom Patrol episode of the first season of Titans is a backdoor pilot. That's understandable since the show and the episode have mostly the same cast and, according to the Wikipedia article on the show,
On May 14, 2018, it was ...
I'm interested in finding out if there have been instances of character crossover in currently running episodes on competing networks?
If you count streaming services are competing for networks too then I will count Crisis on Infinite Earths
In this crossover we have, CW network running shows;
Supergirl (Originally CBS in seaosn 1)
After watching the crisis episodes, IMO I guess you have to definitely watch Arrow and maybe Flash and Supergirl.
ARROW: (Important to watch)
The final season deals with the build-up to the crisis event and also throughout the season hints at
It also explains more about the crisis' effects and about the Monitor and so this season of Arrow is important