Hey if the city is going to let you have wooden floors they probably won't say anything about some cracks.
First off the caulk is gonna look like crap. It's clear not invisible. Second does the tube say paintable, if not don't eeeevvvven bother. Get a good floor guy, have em use a brush in the wide crack and mop the rest. Sealing with poly is better then caulk.
Don't lose any sleep over it. Rustic floors are just that, if that's not what you want then go over them with new flooring, but don't go and do anything silly.
PS White Lightning discolors. Turns a gross looking yellowish color in time.