Can you walk on a partial Achilles tear? And what would the treatment be.

Sometimes. Depends on how the tear occurred, where in the tendon it is located, how big it is, and how active you are. If it is an acute tear, then treatment is generally some type of immobilization, and perhaps some restriction of weight-bearing, followed by therapy. Sometimes surgery is needed. If it is a chronic partial tear, then the treatment can vary, but it is often similar.
Yes. If it is partial tear, treatment is immobilization and non-weigt bearing depending on how much is torn surgery may be indicated.