Nowhere in Blink's description, or the description of the Ethereal plane on page 48 of the DMG, does it say anything about limiting your use of reactions in any way. So yes, you would still be able to use your reaction while on the Ethereal plane.
You can't, however, use your reaction to make an opportunity attack against anyone on the plane you originated from because "you can only affect and be affected by other creatures on the Ethereal Plane" and they are not a creature on the Ethereal plane.
As for Polearm Master, I'd say it would depend on the manner in which the creature enters the Ethereal plane. Creatures don't provoke an opportunity attack when they teleport or when someone or something moves them without using their movement, action, or reaction.
Blink for instance could be thought of as a form of teleportation, but it also doesn't use the creature's movement, action, or reaction to get to the Ethereal plane so it might not provoke an opportunity attack.
Whereas a Ghost's Etherealness ability does use it's action to enter the Ethereal plane so that might provoke an opportunity attack.