It has been a long time since I studied thermodynamics , but by careful design of your material structure I am certain you can greatly increase thermal radiation from part of an object without having to expend any energy which would leaf to more waste heat.
To an extent, yes. The ideal radiator would be a fractal surface with very high surface area, extending well out from the ship. ie, really easy to shoot off.
And like you say, they are way too maneuverable. (Not to mention that they are "trans-Newtonian".)
They presumably still have to produce lots of heat, though - the changes in kinetic energy have to powered somehow.
I suppose a TN drive might work by an Alcubierre warp-drive model (with superluminal travel precluded due to blueshift problems.) Basically, your "engines" would produce a warp field around your ship, and the whole space-time bubble moves. (The ship itself is stationary with respect to local space.) The energies involved would be... immense, but I guess that's why you need sorium fuel.
I think I like this model - it explains the reactionless travel, and it explains why higher tech levels let you move faster and more efficiently. On the other hand, while it might make thermal cloaking easier, ordinary ship movement would show up like a beacon on gravitic (ie, "EM") sensors.
You can maybe explain a cloak by nipping off your spacetime bubble a bit from local space - but that would also limit your ability to see the outside world. And it might also run into some blueshift problems, I'm not sure.