If my Fighter6/Brawler2 wielding her Glaive-Guisarme has an adjacent opponent and no room to 5ft step to bring her weapon to bear, can she use her first attack to Punishing Kick the foe away and then use her iterative to slice & dice?
Yes, you can absolutely do that. Punishing kick alters one of your attacks without changing what kind of action it is, so you can punishing kick as one attack and then use the rest of your full attack.
Okay, I just wanted to make sure it wasn't considered TWF with a two-handed weapon
It would be switching to a different weapon as your next attack in your full attack routine; which is fine.
You can make unarmed strike with any body part so you don't need a free hand for it, and as long as you're not trying to gain extra attacks from TWF then you don't take any kind of TWF penalties. An unarmed strike does not have to be used in TWF at all.
Actually a pretty smart combination. Bravo.
It is legal to make an unarmed strike with any part of your body. In this case, thematically you would kick them (while holding your glaive in both hands) causing unarmed strike damage and potentially moving them back 5ft which would then enable you to use your glaive against them.
As long as you're not trying to get an extra attacks beyond what your normal BAB would grant for iterative attacks you're fine. If you tried to two weapon fight using unarmed strikes as off-hand attacks, you could not use a two-handed weapon since they take up both your primary and off-hand worth of effort. But you're not trying to do that, so it's largely irrelevant.