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If I have a unit on the battlements of a imperial bastion, but none inside it. Can my opponent enter the bastion and claim it while my guys are still on top of it?

Yes .

The battlements are separate.

Likewise they can land on the battlements of a building you control.

Battlements are really no different from the normal terrain surface. With the exception that stuff happens with certain damage results to the area of the battlements and units within. Otherwise its open terrain, so the building is unoccupied.