Who gets the 2 bonus victory points for reaching a new island?
Generally speaking, no points are granted for expanding to an island. 

That said, some of the scenarios have a special rule that grant points for expanding to an island. For example, scenarios 1, 4, 8 and 9 have the following special rule:


  If you build a settlement on a foreign island, you receive a
  Special Victory Point! Take a Catan chit and place it under the
  settlement when you build it. Each player may earn only ONE
  Special Victory Point in this scenario. It does not matter if
  other players have already built settlements on that island.


In those scenarios, every player that builds on an island other than the one on which they started gets 1 bonus point, but only the first time they do so.