First off.. Adamantane is a bad example of diamondoid. A better example would be, well, diamond. That definitely doesn't sublimate.
The idea isn't to have small, independent molecules that can waft off into the air. More likely, the entire nanomachine will be a single, giant molecule that on a small scale looks approximately like diamond, but has more structure at slightly larger scales. (Of course, tool-tips for moving atoms and such break that abstraction slightly, and need careful modelling.)
Yes, carbon-based nanomachines exist already. No, they aren't eating me; humans are some of the meanest nanomachines around at the chemical level; more likely I'm eating them.
No, biology isn't as powerful as artificial nanomachines. Biology has hit local maxima it can't get out of, like using proteins instead of three-dimensional diamond-like carbon bonds for armor. Which are only fragile when you make a single, simple giant crystal instead of one with carefully introduced flex and fracture points that prevent damage spreading.
Yes, nanomachines need energy. No, they don't need as much energy as biology; eutactic machinery avoids a lot of the friction inherent in biological chemistry.
But your last point is completely correct. Nanomachines won't be made to do this; even if it's possible, there's no reason to. Nope, we'll have them eat cancer or scoop up poisons or radiation; there's no reason whatsoever to make them self-replicating, when nanofactories can turn them out by the tonne in a much safer manner.
They won't be making microchips either. That's for the nanofactories.
Oh, and elemental needs - carbon, hydrogen and nitrogen mostly. Exactly what we're made of.. huh, what a surprise. Trace metals, yes, for the tooltips.. same as we use them for. Hmm. One wonders why.