Should I sand my traditional wood floor before staining?
If you sand it you'll eliminate the charming deep grain and rough-sawn artifacts. I wouldn't sand anything but what seems like an injury hazard. I'd also leave the gaps empty. A hard-floor vacuum will keep it clean enough.

To the second question, staining without sanding will give very dramatic color variation in the open grain and saw kerfs. You'll get a nice rustic look. If you prefer a more modern, uniform color, sand it well to an even smoothness after you fill the gaps. 

Having said that, I'm voting to close the question as primarily opinion-based.