Guild Wars 2

So to my understanding, each 1st place winner in each league will receive a dolyak finisher at the end of the season. Does this mean if I transfer over to the server before the end of the season, I could just obtain the finisher just like that?

Nope, you are tied to the server you were on when you first logged in after the first day of seasons.

Nope. The server you logged into at start of leagues is locked in and will determine your reward.