Giant cell arteritis / vasculitis / artery inflammation - could this cause gum bleeding, mouth sores and lesions on tongue as well as lesions on skin?

See below: Not giant cell. The gum bleeding can be related to other dental issues. The other symptoms can be seen in lupus, sjogren's, and behcet's to name a few. However there are diseases that mimic the symptoms of autoimmune diseases and thus you should see your doctor first for an evaluation.

It depends.....: Without knowing your dental status (your periodontal [gum & bone] health, any untreated dental conditions), it would be very difficult to relate these symptoms to your arteritis/vasculitis condition. Gum bleeding is the first symptom of gum disease (gingivitis/periodontitis), mouth and tongue sores/lesions can be due to a multitude of causes. See your dentist and your medical care provider.