Is prolotherapy recommended for autoimmune patients (psoriatic arthrits) or will the autoimmune affects is effectiveness?

Absolutely not. Anything that increases inflammation is going to increase the risk for a flare of autoimmune arthritis. Controlling and reducing inflammation, not causing it, is the basis for most successful treatments with autoimmune arthritis (methotrexate, anti-tnf inhibitors like Enbrel (etanercept) or humira). Strongly recommend you talk to your rheumatologist before starting any new treatments.
No studies. There are no studies using prolo on folks with autoimmune diseases. I have some colleagues that have done it with some success. The risks of prolo are quite few so it wouldn't hurt to try it.
No. Prolotherapy is hypothesized to help with pain and discomfort associated with tendons and musckles.
NO. There are doctors on this site that recommend prolotherapy for virtually any rheumatologic illness. However, the data supporting its effectiveness is sketchy at best and unproven at worst. There is no evidence that it helps inflammatory arthritic disorders such as psoriatic arthritis. Stick with proven therapies that are extremely effective in preventing joint damage.
Not evaluated. I do not believe there are any peer reviewed studies using prolotherapy for psoriatic arthritis so it cannot be recommended. Psoriatic arthritis is a systemic inflammatory disease which needs care by a rheumatologist/dermatologist.