MissingNO is a programming quirk, and not a real part of the game. When you get this, your game can perform strangely, and the graphics will often become scrambled. The MissingNO Pokémon is most often found after you perform the Fight Safari Zone Pokémon trick.
To fix the scrambled graphics, try releasing the MissingNo Pokémon. If the problem persists, the only solution is to re-start your game. This means erasing your current game and starting a brand new one.
I can't find something pertaining to why Missingno. doesn't exist after Gen I, but suffice to say that when Nintendo/ Game Freak got wind of Missingno, they found the programming glitch that caused it and fixed it, since Missingno. frequently crashes games and disrupts graphics/ data. Hence why Missingno cannot be traded outside of a Gen I game, to prevent it from crashing any future games.
While there have been glitch Pokemon in future games, such as Decamarks, they have been incorrectly referred to as Missingno, as it does not exist outside of Gen I games. While Decamarks was an intended creation (it was there to stop games from crashing but not for actual use), Missingno wasn't, and is solely a glitch Pokemon.
Bulbapedia on Missingno.
Nintendo consumer advice