Would some who has psoriatic arthritis and HS be able to have this completed or will it be a problem with an autoimmune problem?

First and foremost, congratulations on your weight loss! Losing that amount of weight will change you life, and you will reap the health benefits for years to come.
The short answer is yes, it is possible to have plastic surgery with a history of psoriatic arthritis. I have performed surgery on many patients with psoriatic arthritis and they do just fine. It is important to have a medical history and medication review performed. Some of the medications to treat psoriatic arthritis can affect your wound healing, and need to be tapered or held prior to surgery.
In addition, require that patients within 10-15 pounds of their goal weight, and that their weight has been stable for at least 3 months prior to surgery.
Hope this helps.

This should be fine, but keep in mind, for best results, it is recommended to be at your ideal or stable weight before getting a sculpting liposuction procedure. Liposuction is for sculpting and defining and removing problem areas that cannot be removed with weight loss and diet / exercise alone. With skin laxity, a tummy tuck or lifting procedure could be performed at the same time as a hi definition procedure. I recommend a hi definition procedure like VASER liposuction. I use VASER HI DEF with ThermRF and fat grafting to get the most fat removal, skin tightening, contour and definition. This combination will give you the most toned result. I recommend getting a formal evaluation with a hi definition physique expert. Best, Dr. Emer

I don't think this is an issue at all. Clearly the specifics of your situation would be discussed with the surgeon prior to proceeding.

Surgical risk is certainly increased with any autoimmune disease, both from the disease itself and from any treatment you may be on.  The key to lowering risk is to have good coordination between your medical and surgical doctors.  In most cases procedures can be safely and effectively accomplished with minimal increased risk.

When one loses weight but does not detox, chemical toxicity can become a problem.  The cause of most autoimmune disease is either chemical toxicity or intracellular infection.  I would recommend detoxification of both hydrophilic and hydrophobic chemicals as well as heavy metals to regain your health.  Most doctors do not know about this aspect of our health as it is politically incorrect.