ITP being an auto-immune disease, would a diet with less vitamin A, C and B6, proteins and probiotics to reduce the immune response be useful?

No. ITP is an autoimmune disease in which platelets are destroyed and maybe even inhibited in production. Depending on the platelet count and clinical findings treatment can range from observation follow-up to multiple drug regimens. Dietary changes other than a well balanced and nutritional diet do not help.