Does it work on cluster and proximity mines, or just bombs that are dropped with maneuver dials?

Either. Action: bombs are still bombs - which are defined as 'things which you equip in the Bomb slot'.

Any bomb, bombs that detonate when overlapped are still bombs, and their tokens are still bomb tokens. They're often lumped into a sub-category of mines when people talk about them, but in game rule terms that doesn't really exist (and even if it did, they'd still be bombs).

As others have said on the forums:

Mine = Bomb

Net = Bomb

Detonator = Bomb

Charge = Bomb

Beautiful.

Cluster mine is three tokens, or one?

Three. If somebody hits all three of them, you only get to Sabine one. On the other hand, if they get overlapped in different turns, you can Sabine them all.