Muzan was ultimately defeated by the collective efforts of Tanjiro, Nezuko, and the other demon slayers. Their teamwork and perseverance were key to ending Muzan's reign of terror in the manga.
One common theme is the exploration of femininity in a typically male - dominated character. Since Muzan is male in the original, making her female in fanfiction allows for a different take on power and how a female demon might rule.
I'm not sure if there is such specific 'muzan x tanjiro mpreg fanfiction' available. Fanfiction can cover a wide range of themes and pairings, but this one might be a rather niche or even against the general tone of the original work in some ways. You could try searching on some large fanfiction platforms, but don't expect to find it easily as it may not be very common or might be against the platform's rules if it contains inappropriate content.
Muzan's origin story is quite dark. He was a human who was turned into a demon through an experiment in the past. This transformation made him the first and most powerful demon. He then began his quest for immortality and started creating other demons, often by infecting humans with his blood.
Yes, there are quite a few. Some focus on an alternate universe where they have to team up for some strange reason. For example, in one fanfic, they have to face a new common enemy that is even more powerful than Muzan. Tanjiro has to put aside his hatred for a while to deal with this new threat.
They could interact in a very confrontational way. Michael Jackson, with his kind heart, would likely be appalled by Muzan's evil deeds. He might use his music as a weapon to try and drive Muzan away or at least make him see the error of his ways.