It seems odd that out of all the alien actors/actresses, Kay suspects the Astro-Tots to be the culprits. However, just because they look cute/friendly doesn't mean they're nice. Also as Kay states, the alien actors who do work on horror movies or crime movies even if fictional, would know that targeting high-profile actors would bring unwanted attention to themselves.
It's a bit odd that many dangerous alien criminals would make their presence known on Earth, and challenging the organization that protects it. Until you ask yourself who would benefit from all these criminals coming here, who just so happen to have extraordinary abilities that can be harvested, and/or fighting the Men In Black to learn their strengths and weaknesses. Maybe a certain corrupt ex-leader of the MIB, Agent Alpha, had a hand in this.
It's understandable why Kay doesn't let Jay drive the LTD. If the Future Jay from "The Head Trip Syndrome" used Time Travel to warn his past self about not using the device that caused his head problem, who's to say that Future Jay or Future Kay warns Past Kay about that incident and with "The J is for James Syndrome", that might be for the best until Jay is seasoned enough.
In a Call-Back to "The Head Trip Syndrome", it might be because of that incident that Jay was able to locate the hideout of the Bug Queen.
We saw less of Agent U until he disappeared in later seasons. Kay's overall interaction with U speaks for itself. Kay assesses that U is not that good of an agent, which may have been the reason for Kay's judgement in picking Jay in the first film in the first place. Jay may not follow protocol, but he does stop and take time to question certain things or assess the situation. While the Arqullian may have been a criminal in disguise, but Jay took the effort to be sure if it is helps to prevent galactic incidents. Since Jay was the first to notice the infection in "The Bad Seed Syndrome", while U remained oblivious until it was too late, it further proves that fact is correct.
Elle became more snarky compared to the earlier seasons, but this aligns well to how she was in the first movie. Her calm and nice persona is just an act to get Zed to let her be a field agent. However after several failed applications to become one, Elle finally has had it leading to her outburst on Zed. Zed now sees what she is really like, so he finally lets her be a field agent, only to pair her up with Agent X. Zed might have found it appropriate to have Elle experience how everyone felt to have an Insufferable Genius standing by your side.
Since the Queen favored Edgar, it makes sense that she wants to honor her late son by reminding her children how Edgar nearly obtained victory for them.