alright here I go to try an answer a few:
First- usually events come back every year at the same time (urf, Hexakill, Xmas), but some are just a rare one time thing (nemesis, mirrior match, 2v2, ascension) that may be a special one time only event or may or may not come back. Seeing as Doombots was on July 17-22 I doubt itll be back for awhile. They are currently gearing up for the Bilgewater event.
second- Legacy skins come out during events or rare times when riot "opens the vault" and this may only allow a certian number of skins to be bought.
third- IDK what you mean by "request" a skin. Riot will give you a small amount of RP for drawing a champ or something, but they wont give you a skin.