So, like vanilla rules, here is no time dependance? You can got ethereals or mutons in jan'1999 in 10% cases? Or specific race should "arrive" at first?
Theoretically, they could, but it doesn't work this way. As indicated by the comment in the section of code, all retaliation missions generated from a shotdown UFO will use the race that was in that UFO and ignore this list. These particular raceWeights only come into play if a missionScript is set to generate a retaliation mission. FMP doesn't add any such scripts as far as I've seen and thus only the vanilla retaliations come into play, one from completing "The Martian Solution" research and the other is on a difficulty-based months-passed condition. On superhuman, that's after October'99 has passed.
2. Do labels (numbers) in RaceWeights section actually represent months?
Yes, and the engine will continue to use those weights until the next month threshold has passed. If no further months-passed are set, then it'll use the latest one in the list (in this case, 0) for all future months.
3. Can specific alien base race change during the game? IIRC seeing snakes + chryssalids on early scouting mission, but then I finally got my toys and balls one year later for another visit, it was turned to be populated with mutons instead... Or I just messed my memory with another campaign?
While OXCE has added such modding option, FMP has not been updated to use it. So, no, they can't in this mod.