When doing things like setting TDC or just random testing (of the timing chain/belt, for example), does it matter whether the crankshaft is rotated clockwise or counterclockwise?
Hardly ever. Most turning should be done clockwise. If you need to rotate it back a few degrees to get it to the specific TDC point, it's not an issue. This will not cause any damage to your engine. If using the main bolt in the end of the crankshaft, you do run the risk of it loosening when turning it CCW ... but that isn't a big deal either. Just tighten it back up by cranking it back over CW, then get the crank back to where you want it to be. Usually if done easily (no sudden jerks), the bolt in the crankshaft will not loosen and is a good place to rotate the engine from.
Even if your cams are gear driven it should be in the same direction as normal operation, but chains especially have a "slack side", and under load it is slacker than you think. When refitting timing belts and lining up the scribe marks you should be torquing the crankshaft in the normal direction of rotation. You don't want to be out by one tooth.
Be careful never to rotate the crankshaft out of the "safe zone" if the camshaft is decoupled.
For timing, and if the chain is suspect, better to test with a light while it is running (as it may be jumping around in this case) a road test may be the best method of tweaking.