Base Mastery

You can activate Overwhelming Presence at any time during an encounter. The wording 'at the start of an encounter' is intended to indicate that you can't use this ability before and encounter, not that you can't use it in the 2nd or subsequent rounds. In other words, you can't walk around with this ability 'always on', you need to take an action during the encounter to use it.

The benefits last until the end of the encounter.

Overwhelming Presence 3

This should be considered to work in the same way as Improved Feint base mastery, which is:

"You can make a Bluff check to feint in combat as a move action without suffering the challenge penalty for using a skill faster than normal."

So, in effect:

"You can make an Intimidate check that would normally be a standard action as a move action without suffering the challenge penalty for using a skill faster than normal. This ability has no effect on Intimidate checks that normally take an amount of time other than a standard action."

As an aside, I personally only allow fast completion to reduce an action to swift, rather than free. Just as a general 'sanity check' thing. But I do allow any action to be reduced two steps (rather than only move actions being able to come down to swift)