Health deterioration causes depression?

It certainly can! No one wants to be less than healthy. Add to that the genetic component to major depressive disorder, and the likelyhood of depression rises.
Absolutely. Depression is common in many chronic health conditions, such as heart attack (40-65%); coronary artery disease without heart attack (18-20%); parkinson's (40%); ms (40%); stroke (10-27%); cancer (25%); and diabetes (25%). Depression also worsens outcome in all these conditions. It's more than psychological -- some feel inflammation may underlie depression as well as these other conditions.
It can. Depression may be related to loss of good health becouse the same problems are effecting brain chemistry, or despondency secondary to the loss. Either way treatment is indicated.