So I understand free actions cost actions during the actual Working Together, but, can things like Perplex and Outwit, be used post Working Together? Second question, could I use Perplex before Working Together?

Thanks,
Arc

Yes to both, you can use Perplex/Outwit, kick in your Working Together, then use Perplex/Outwit afterwards if you still have it available as long as you didn't use it earlier.

You can use a free action before, during (using a free action to do so), or after working together.
I don't know of any cases where that gives you an extra perplex or outwit per turn.