Yeah, Problem 1 definitely is a (very difficult) open problem, not likely to be solved any time soon. Problem 2 just looks to me like a known fact, not really

Yeah, Problem 1 definitely is a (very difficult) open problem, not likely to be solved any time soon. Problem 2 just looks to me like a known fact, not really a problem... and Problem 3 is only a problem if you don't accept the standard definition of "elementary", and/or if you worry too much about leftover pieces. As soon as you can see two separate pieces inside a larger spaceship, and each of the pieces in isolation would travel at the same speed as that larger spaceship, then that larger spaceship is not an elementary spaceship. Once you take out the recognizable pieces, there may well be sparks and other junk left over. But they might just be side effects of the interaction of the recognizable pieces, not anything that can function independently. There are way too many such fading sparks and such for each one to deserve its own name. Minor side note -- no spaceship of any size will ever contain a Garden of Eden, because every spaceship by definition has at least one predecessor (itself).