Bluff and the Devious Manipulator Feat

Q: What kind of action is using Bluff with the Devious Manipulator feat?

The Devious Manipulator feat doesn't change the type of action required to Bluff. It would depend on what kind of bluff you were attempting. See page 82 of the rulebook for the typical actions required by the Bluff skill.

Playing Dead

Q: Can a character fake his own incapacitation or death, in order to throw off opponents, or to allow a berserker ally to gain the fury bonus from a fallen friend?

I'd certainly allow the attempt (both to fool an enemy and to fool the berserker), with circumstance modifiers based on the conditions (if you still have 50 hp, I'm putting a big negative on there) and how often you've done it (since the berserker will catch on eventually).