When does intellect prevent our awakening?

Intellect can be said to interfere with the attainment of enlightenment when it leads to delusion. What is delusion? It is a belief based on something that is not true.

"Just stop!" But before, or after awakening?

Perhaps the number one mantra in all of modern Western spiritual teaching is: "You are already awake, you just don't know it. Stop everything and let go,

What exactly is enlightened awareness?

We experience the full spiritual awakening, or enlightenment, when we are no longer the witness. That's because the witness creates duality.

How do we know when we are awakened?

We know we are awakened when the teachings become confirmatory of what we already know. When we go to satsang we no longer learn anything but 

What is the relationship between mind and awareness?

Mind and awareness should not mean the same thing. If they are used interchangeably they become less useful.