This combination of preexisting medical conditions could definitely be a potentially serious health risk, and each one could also aggravate the next.
Uncontrolled High blood pressure could lead to more bleeding during surgery, and if you are already anemic this could lead to having to do a blood transfusion. Also anxiety and depression could become worst in the postoperative period and could play an important role in elevated blood pressure levels putting you again at a higher risk for bleeding.
So first thing is to get this conditions under control and have a detailed preop evaluation performed months ahead of time.
No aesthetic procedure is worth the risk.