6 years ago - Mr. Mxyzptlk firs appears in Metropolis to torment Superman, until he discovers the secret to banish him back to his home dimention.
4 years ago - Mr. Mxyzptlk appears a week before Clark Kent & Lois Lane's wedding to torment them, but ultimately he wishes them well.
now - Mr. Mxyzptlk appears on Warworld during Clark Kent & Lois Lane's imprisonment, taunting them with false rescues.
If it isn't already very clear... golden age comics were very much for children. These are the stories that laid the groundwork for everything comics would later become, but at the time these were not meant to be taken incredibly seriously. If ANYTHING is exemplary of that, it's Mr. Mxyzptlk. a "5th dimentional being" with limitless reality-warping powers that came to Earth to torment Superman until he tricked him into saying his own name backward. If the fanciful parts of comic book stories strain credibility, Mxyzptlk downright jettisons it. Still, Mxyzptlk is a long-standing part of Superman's lore, and he presents a particular challenge for any writer to incorperate him into Superman's world.
Mr. Mxyzptlk's Comic History
Mr. Mxyzptlk appeared for the first time way back in 1944. He's appeared over and over in countless formats, on every animated version of Superman, in every live-action series, and in every single new continuity of DC comics.
In fact, he's even appeared in the actual Marvel 616 universe, where it was revealed in continuity and on-panel that longtime Fantastic Four villain was actually Mxyzptlk visiting a differenct universe with a different appearance. Personally, I like to imagine that he's also the Great Gazoo, meaning he's also pals with Fred Flintstone.
Our Mxyzptlk Story
Mxyzptlk's motivation has pretty consistently been just to torment Superman. He has occasionally had designs on world domination, or on marying Supergirl, but in the long run the conceit seems to be that his main utility is as a nusiance, so that's how we're going to use him.
The usual understanding of Mr. Mxyzptlk is that when Superman tricks him into saying his name backward he's returned to his home dimention for 90 days (although there were periods after the first crisis when he and Superman would have different agreed-upon conditions each time he appeared). Because we're structuring out a timeline, it actually helps us to extend that time in order to create certain specific occurances when the character appears. He's a very weird story element, and by making the time between his appearances two years instead of 90 days we get to keep those appearances limited and thematically focused. The week before Clark and Lois's wedding and during their Warworld imprisonment are great periods to introduce this sort of chaos into their story.
Also, we decided to create one story where he is tormenting the entire Watchtower... because that will be hilarious.
Believe it or not, there are actually two schools of thought here.
The most common pronounciation is "mix-yes-spit-lick". This is used with a few teeny variations in, among others; the 1940's animated serials, the 1980's superboy series, Lois & Clark, the Superman Animated Series, Smallville, Brave and the Bold, DC Universe Online, and Supergirl.
Meanwhile, The classic animated Super-Friends series pronounced Mxyzptlk as "mix-ul-plick", cutting out some of the sounds. Comic legend and noted Super-Friends devotionist Alex Ross advocates for this pronounciation, but virtually all other creators seem to reject that idea. In fact, in the Superman Animated Series Clark tries to read the name before he hears it, and uses the Superfriends pronounciation. Mxyzptlk appears and admonishes him for getting it wrong, and lays out a very clear pronounciation guide that used visual cues. Series creator Bruce TImm actually mentions Alex Ross's Super-Friends obsession in the commentary for the episode, so it's fun to imagine that the entire bit about correcting the error was directed at Alex Ross himself.
Mxyzptlk's original appearances were of a small cartoonish round-headed guy in a purple suit with spats and a bowler. During the early eighties when there was a big push to give all the villains a more science-fictiony look (Lex's battle armor, Brainiac's android body) Mxyzptlk started wearing a orange jumpsuit with purple trim, and started sporting his trademark pointed grey hair. Later versions seem to be favoring the suits, and sometimes make him look more impish or fae-like, although I'm not sure how much I like that.
I happen to like the suits, and am a bigger fan of his big round head. The character is CLEAERLY meant to be a living cartoon, and if you try to disguise that you're just acting like you're ashamed of him. Just use him as a cartoon. He's fun that way.