Are the Irish ‘bean’ (woman) and the Hindi ‘bahan’ (sister) cognates from Proto-Indo-European?
Damn, this one took work. No.
Hindi bahin or behin is from Middle Indo-Aryan (Prakrit) bahini, from Sanskrit bhagini, feminine of bhagin, “the happy or fortunate one”, from bhaga, “fortune”. Signifies “sister” and secondarily “woman” or “wife”.
Irish bean is from Proto-Indo-European *gwen, woman (cf. Greek gyne).
When come back, bring Proto-Indo-European. 
You know, that version does sound really like an order for takeaway food. When you’ve got several people, all failing to decide what shop to order form.
Very very interesting question and answer, btw.
<Departs singing “when Irish pies are smiling…” >