Is the damage from special crossbow bolts calculated the same way as the relevant spell (i.e. scales with magic power)?
That would seriously depend on what you're talking about. Most, like fire bolts, poison bottle bolts, etc, etc, don't. A few, like squid bolts, do. But the proportion is skewed enough to say safely that you shouldn't expect it.
That much I knew - I've skimmed the XML files. Just making sure that when the bolt procs, it behaves like the spell effect -- that the magic power value used is indeed the player character's magic and not some crossbow-adjusted substitute. Which leads me to the question...why? Seems the characters most likely to benefit from this calculation (spellcasters) are those least likely to need/use it as a source of ranged damage.