increased PTT + hemarthroses + easy bruising = Hempophillia A which is a deficiency of Factor 8 and is XL recessive (ie why the mom's brothers have it)

Vwf deficiency can also present with bleeding and increased PTT but its autosomal dominant so the male wouldnt be only affected. Vwf deficiency is the most common inherited bleeding disorder

The answer is factor VII because it has the shortest half-life of all the Vit K dependent coagulation factors. Warfarin inhibits epoxide reductase -> no more activated Vit K -> no more activation of coagulation factors 2,7,9,10,C,S -> factor VII degrades first =(FA 2018 p 402)