1) There are several members here who have expressed an issue with this, loudly and often. I have not been able to find any image I have taken that I can say shows this phenomenon. Maybe it affects a small sub-set of cameras or there is some other issue but few people seem to have any problem with it or are even able to see it.
2) I've never used the video function so no help
3) Crappy old film era junk is still crappy old film era junk. Good film era lenses hold up quite well. I have a mix of Pentax-A, Pentax-F, Pentax-FA and DFA lenses and the new modern zooms are in general better than film era zooms. But top end film zoom lenses and most film era primes are excellent on the K-1. And most film era lenses are far smaller and lighter.
4) I have not had any issue with the remote socket. Seems as solid as the one on my K-3II. And yes the C-205 type remotes work. As do most remotes designed for Canon.
5) It isn't noticeable all, unless you are shooting off bursts.
6) That can be done but I question the utility. Seems far simpler to just shoot four frames, moving the camera between and blending the frames in LR or PS. I might be wrong, but this seems to me to be one of those things are that are really cool to do, but have no use in the real world. of course I might be missing something and if so I'm sure someone will let me know