Hardwood flooring nails showing through plywood from underneath
Most of the time, anything that's fastened to plywood is required to have the nails penetrate beyond flush with the lower/back face of the plywood. This is to give maximum grab to the nail shank. What you're seeing is perfectly normal and expected. Other examples are roofing shingles and vinyl siding.

The wood debris on the floor is a result of normal vibration causing slivers to drop over time. It's not cause for alarm, and to prevent it in the future do some brooming or otherwise rub down the underside of the subfloor to knock the slivers off all at once.