does it come with the stand?

It is just the pad, stand is bought separately.

will this pad fit other elevated dog beds?

Your question is confusing? We purchased this dog/cat bed and the sheep wool cover fits it fine, and our dog loves it. The pad came with the bed as a kit. Does it fit other elevated beds, if same size yes. You have to match pad with bed size.

Will this fit the original bolster raised bed in large size?

Yes. It has elastic straps on the corners that go under the legs to hold it in place. The bolster has the same type of elastic straps and fits back on over the mat. Fits perfectly & our dog loves it.

Would the medium size fit the large cot with the bolsters?

It would lay on it but if you have the large cot the large pad would actually fit the same dimensions and the elastics would be able to go around the legs to stay in place. A smaller bed than cot wouldn’t be able to do that.