If the adept's target has partial cover, do TN's go +4?
Do visibility modifiers apply?
Target running +2?
etc.

If cast through a clear non-astral barrier, does the barrier reduce the power?

I'd welcome your thoughts on this.

Those all sound like good ideas to me.

I might even say that an astral barrier should block it as well, just because that sounds sorta cool.

Yes, it's treated as a normal ranged attack. Ranged attack TN modifiers apply. If there is an interposing barrier the attack must penetrate the barrier just like a bullet or arrow.

The text also specifically says that astral barriers impede the use of this power, as I recall.

If you get anal about the rules, it states that you make an Unarmed Combat test as normal, hence the modifiers for unarmed combat aplly. Only the unarmed combat modifiers apply (except reach, which they specifically state is not counted).

This basically means that as long as an adept can see you and you are within his range, he can transmit an attack against you. I am fine with this ruling since 2 pts is a lot to plunk down just so you can punch people who are within 18ft of you, so you might as well grant some lenency with the modifiers.