Blue Gremlin can teleport even if Unmovable or Restrained. The source doesn't matter for that.
So this means CURRENTLY:
WILL the Blue Gremlin set off traps? YES, it still enters the zone
WILL the Blue Gremlin be able to teleport thru a wall with no LoS(like a stone wall)?YES, because teleporting does not require LoS - although the incantation Teleport does require LoS ("target zone").
WILL the Blue Gremlin take a passage attack from a wall with the trait?NO, because it teleports past the wall
CAN the Blue Gremlin move out of a conjuration of effect that Restrains him? OLD rules said NO (because BG cannot move and therefore not teleport) - CURRENT rules say YES (because it teleports instead of moving).
WILL the Blue Gremlin be hindered ?OLD rules said YES (because BG teleports as a *move action*) - CURRENT rules say NO (because its move action has become a *teleport*).
CAN the Blue Gremlin move 2 at a time, bypassing a zone enchantment for example ?NO, because moving 2 zones really consists of 2 individual move actions that are in the case of the BG in fact teleport actions. So the BG teleports out of its current zone and touches down in the first zone that is next to its current zone before teleporting a 2nd time to the 2nd zone that is next to the first zone.
Did I get it?