FAQ

The movie would suggest that it is possible, but likely rare, for former agents to come back, and go through a deneuralyzer to return to duty. This would allow a highly experienced agent (such as Kay) to re-access all the information they acquired over the years, rather than have to start over. Otherwise, why would MiB headquarters have one?

Furthermore, it is likely that the deneuralyzer at MiB headquarters is a fully functional one that would have worked flawlessly, allowing Kay to reacquire all his former memories (including the locker). This, as opposed to the only somewhat functional machine that Jeebs had, with limited results.

The one at headquarters could also be used for witnesses that were neuralized, but further questioning was required.

After Jay neuralizes him, he tells the clerk to move out of his mother's house, due to him being so old. The implication may be that the clerk's mother is very controlling and dominating, so he's never felt he's had the freedom to simply be his own person. So the neuralizer, may have unwittingly unlocked the clerk's true desire to be free from his mother. Unfortunately this may mean he only feels he can be free from her if she's dead. So he was going to use the shovel to kill her and bury her.

All that being said, it's supposed to be a brief and darkly humorous moment.

Men in Black II, like its predecessor Men in Black (1997), is taken from a script that is based on a Malibu comic book series called The Men in Black by American writer Lowell Cunningham. It was followed by Men in Black³ (2012). Men in Black: International (2019) is a spin-off movie.

It doesn't. Men in Black: The Series (1997) was made after the first film but before the sequel, and they are not meant to form a single, coherent continuity.

Apparently, the MIB agents arrested him.

The movie implies that he is but never makes her paternity explicitly clear.