Can the rear stut rattle and still be functional

If by functional you mean that it's still bolted in place and holding the suspension together then yes, but that rattle that you hear is the strut rod inside the cylinder bouncing up and down really fast with no resistance so it really is not functioning at all.

This depends on what is loose. It can be the source of the rattle but is doubtful. Start by checking for loose components with the car sitting on the ground as well as jacked up. Some components may only rattle under certain circumstances.

Sure but its bad change both rear struts as a bad handling sitruation can come up and you'll lose control of the car.. All of the struts are likly to be bad if the car has over 100 thou and chaning just one will cuse a handling balance ptoblem.