This seems like a two part question.
I've seen a starship take control of another starship remotely, given the appropriate command codes, etc. It stands to reason a shuttle and possibly an escape pod may be capable of the same remote control; and if not, surely they could be modified to do so.
I am sure they could, I think we have seen a little bit of it in Insurrection while data was freaking out. Shuttles generally do not have lots of firepower, so they would essentially just be using the warpcore. I imagine the output of a shuttle warpcore is on par with a photon torpedo, else we would see this more often.
Why not just launch a shuttle at a borg cube, etc. at warp speed? The possible effects of a warp field colliding with a target could be huge; but surely the subspace field and the momentum would cause a large hole to tear right through it. Why don't they try this as a last resort?
The thing you have to remember, is how warp works. They use an Alcubierre Drive. You are essentially moving slowly through space, and moving space faster than light around you. The velocity of your ship is sublight, therefore, the net mass of your ship is effectively the same. This is how they get past the lightspeed limit. At that point, again you are just throwing a huge mass at slow speed into the enemy, and most of the damage is from the warp core. Still massive, and we do see this in first contact.