Dave Springford wrote:

My club is buying a K-21 for student training and I am wondering if a
tail dolly is necessary for ground handling?

It depends on what you call "necessary" and how your operation works. It
definitely makes ground handling easier. For me, it's worth the
(comparatively small amount of) money.

When empty, does it sit on the main and tail wheel, or main and nose
wheel.

Tail wheel.