Probably not quite enough action to qualify, but there are the Torchy Blane films from the 30s (which influenced the creation of Lois Lane).
https://en.wikipedia.org/wiki/Torchy_Blane

First travel to a parallel Earth - live action TV:
Parameters: A character must make a trip to a world that's not his or her own. Simply showing a world where the Nazis won the war from the perspective of its inhabitants is not enough. For now it's enough to just have it be live action TV in general. Should it prove to be in an anthology show, I'll add a separate category for ongoing characters.
Suggested answer: Star Trek: Mirror, Mirror, in which Kirk visits the Mirror Universe 1967

First travel to a parallel Earth - animated action TV:
Parameters: As above, but in a cartoon
Suggested answer: Super Friends: Universe of Evil (1979), in which Superman visits said universe

For now I'll leave it as the above. But Hopefully for at least one of the above someone will have an answer that isn't just "evil version of main universe". If not I'll create a "non-evil" category later.

We should also consider the same "first travel to a parallel Earth" for prose (novels or short stories), comics and films. And to clarify, while handbooks count alternate futures as parallel Earths (because by the way time travel was originally established to work in Marvel they were), we should not count cases where this wasn't the original intent - e.g. no including time travel to the future or past in a story UNLESS the story makes it clear this is an alternate reality. Also no counting of traveling to fantasy worlds UNLESS they are explicitly alternate versions of Earth - so Dorothy going to Oz (which I've seen some say is an example of traveling to a parallel Earth) does not count, but the travels in Incomplete Enchanter to places like Asgard do count because the story makes it clear this is traveling to alternate realities.

Just to clarify further (and my use of "Earth" should probably be "universe"), I'm not referring simply to other realities with completely different lands, but universes with clear similarities with the main universe. So Oz wouldn't count even if it was explicitly in another reality unless it was further explicitly stated to be Australia or somewhere else. You can't say for certain that the Emerald City is definitely where the centre of Australia ought to be or why it's surrounded by a lethal desert instead of the sea, etc.
 

Andy E. Nystrom wrote:

Just to clarify further (and my use of "Earth" should probably be "universe"), I'm not referring simply to other realities with completely different lands, but universes with clear similarities with the main universe. So Oz wouldn't count even if it was explicitly in another reality unless it was further explicitly stated to be Australia or somewhere else. You can't say for certain that the Emerald City is definitely where the centre of Australia ought to be or why it's surrounded by a lethal desert instead of the sea, etc.
 

Yes, I concur. Oz shouldn't count anyway, as the implication seems to be that it is somewhere on regular Earth, given it can be accessed by balloon. But other realities that are not parallel Earths wouldn't count. That's why myths where people go to Olympus, Asgard, the Celtic Otherworld/Faerie realm would not count, but Incomplete Enchanter were they go to Asgard and explicitly state that the supposed mythical reality is really an alternate reality would. 

Andy E. Nystrom wrote:

First comic book protagonist death - later reversed
Parameters: The lead of a comic book feature is killed off, though later brought back
Suggested answer: The Comet: Died in Pep Comics #17 December 1941; brought back in the 1960s. There is little doubt that he's the first superhero to be killed off, but it's possible that a non-superhero lead was killed earlier.

Got one that beats this. Cat-Man debuted in Crash Comics#4 (September 1940), and died that very same issue!

Cat-Man may also be the first case of a character being resurrected (where said resurrection wasn't part of their origin), as he returned from the dead the very next panel:

Nevertheless, he was genuinely dead, so it still counts as an example of a lead character being killed.

Andy E. Nystrom wrote:

First comic book protagonist death - never reversed
Parameters: The lead of a comic book feature is killed off, and remains dead
Suggested answer: 711. Killed in Police Comics #16 (January 1943). Never brought back.

Perhaps a bit of debatable case here, but in Silver Streak Comics#9 (April 1941) the Claw burns his nemesis Daredevil to death. It subsequently transpires that this was not the original Daredevil, but his brother, covering for Daredevil while the hero was on holiday. So the debatable bit is whether the fill-in Daredevil would count as the lead - some might say yes, albeit very temporarily, others would insist not - but if he is, then given that he stayed dead, he'd beat 711.

So, um, er, it's come to my attention that there have been multiple superheroines that have been powered by, uh, the time of the month, the most recent one promoted because Games of Thrones' Emilia Clarke created the character. So...

First superheroine to be powered by time of month.
Parameters: Can be any media but that has to be the source of their powers, and it has to be that monthly occurrence and not anything else that happens monthly.
Suggested answer: Ms. PMS, star of a short lived 1992 comic series.

And to move on to a probably more comfortable topic:
First confirmed appearance of the Earth-1 Batman.
Parameters: Not actual first appearance because that's impossible to determine, but first instance where there is no ambiguity on the matter, where there is no possible way it can be the Earth-2 Batman.
Suggested answer: As I noted in the Non-Marvel Getting Wrong thread, the first New Look story is often suggested, but there's an earlier example: Brave and the Bold #28 March 1960. This was the first appearance of the Justice League. The Earth-2 Batman was a member of the Justice Society, not the Justice League, so the Batman in that comic in unquestionably the Earth-1 version.


 

Spinning out of a FB discussion where I apparently really upset the other person by disagreeing with/correcting them. Someone stated that the Clock was "the first masked crimefighter in comics"; I contested that while he might be the first in a comic strip, or the first in American comics, he was not the first in comics overall as there existed at least one earlier example, Batsowl. He was definitely masked, as evidenced by the illustration included in the link, and he appeared in a British comic, Illustrated Chips, though he himself appeared in a prose tale with limited illustrations. Not wanting to concede, the original poster insisted that Illustrated Chips wasn't a comic by the American definition, but per the American dictionary Meriam-Webster a comic is a "magazine containing sequences of comic strips" and Illustrated Chips was definitely that:

Anyway, we're now after:
First appearances for masked crimefighters/vigilantes/seekers of justice, who may or may not be superpowered, in various media. The character has to be masked as a regular part of their outfit, so examples where someone adopts a mask temporarily do not count. Afaik, the following hold the titles at this moment, unless and until an earlier example arises:

First in prose fiction: Spring-Heeled Jack, 1968. The character appeared in legend and in Penny Dreadfuls several decades earlier, but the 1968 iteration was the first that I know of to be revealed to be a normal human in disguise rather than some demonic entity.
First in a comic book but not a comic strip: Batsowl, Illustrated Chips (1918)
First in a film/film serial: The Masked Rider, The Masked Rider (May 7th 1919)
First in American comics: The Clock, Funny Picture Stories#1 (November 1936)

I will note that, unlike the poster I debated with, I am more than willing to be corrected if/when others locate earlier examples.