Question: Boris used the first time jump device to go back in time to 1969. J used the second one. You see throughout the movie that J has his with him for obvious reasons. But you never see what happened to Boris' device. So what did he do with it?
Chosen answer: He probably just put it in his pocket until he needed it again to go back to the present. Most likely, it would have been destroyed when 2012 Boris was killed after he was burnt by the space shuttle.
Question: O says that back in Cape Canaveral, in the unaltered time line, something happened to K that changed him. All that's really said though, is that he stopped and arrested Boris the Animal there. So what exactly was it that changed K?
Question: It is told that J remembers the events of the regular time line because he was involved in the past. Being there as a young boy that is when his father was killed. So why does O not remember the original time line? She was there too, as K's lover.
Chosen answer: O was not at Cape Kennedy for the launch, that was the focal point of the change in the timeline, so only people there would remember the original course of events.
Question: When K is killed in the past, why is it that nobody remembers K (beyond '69 that is) but J remembers everything as it once was?
Chosen answer: This is answered in the movie by the character that gives J the time traveling device. The character tells J that he can still remember K because he was involved in the events. The young black child at Cape Canaveral was a young agent J. So he was there and at least passively involved.
Answer: He meant that adult J already time traveled. In the 1960 's, K met J for the first time, when K met Detective James Edwards that was the second time, which is why he had him apply for MIB.
Chosen answer: Most likely "Intergalactic Department Of Corrections."