Carbon dating - is this available for mere mortals, or even what I need to date an old building?

Yes lots of old nails, and hooks in the wall. Of course, they could be from any time in its history.

I did notice a couple of large nails with square heads sticking out of the wall that look hand made - a quick google tells me they’re likely pre-1800, although that would align with the age of the main house so not many surprises there.