1. Regarding places with questionable dates /times there is a difference between staying there (מקום יישוב) vs passing through. Note that the first אג"ק to discuss this (תש" ט) makes this distinction between the boat and arrival in Australia...
2. Sefira is supposed to be counted after tzeis. No bracha is made in those other locations.
3. AFAIK satmar follows some of the later shitos for tzeis (for sure RT not AR/GRA)
1. That letter is something else entirely. The question there was not whether it is day or night, but which day of the week (Shabbos). Day of week is not an empirical fact, i.e. there is nothing in nature or astronomy to say its Monday or Tuesday, (i.e. days are just clones). Rather, days of the week are a human convention, i.e. people decide what day is Sunday, Monday … Shabbos, (hence places where people changed day of the week,
with a recent example here,) and why a Dateline became necessary, and lehavdil, for Jews, all of that is with the Koach of Torah. It is about this that the Rebbe says (as expanded more in various Sichos, and LA’s Rosh writes about it at length in Migdal Ohr) that there is a connection between Shabbos and the way it was first established (perhaps even unwittingly) by the first Yidden who lived there, and hence the dilemma for one who is in a place without a community, or passing very briefly through a place with a community.
However, day / night is an empirical matter and has nothing to do with human convention. Therefore, whether there is a community and how long you stayed is irrelevant. This is true even in the Polar according to the Shittos that day / night is determined by the position of the sun (which is certainly the Rebbe’s position), day / night remains an empirical matter, and not subject to human convention. Thus, the above letter is not relevant here at all.
2. Incorrect. Sefirah is counted at לילה. In “normal” locations, Tzeis is לילה. In unusual locations, it may be something else… in fact your next point demonstrates this… did the Jews of far Northern Europe who followed RT not count Sefirah?
3. Correct, but I believe they do this as 72 minutes and not 16.1 degrees.