As for the House of Osman... If Selim manages to cling to life he might be able to sire a child or two, but the tradition of brother killing will have to be put on hold since there's too many risks of the house dying out because of it. Maybe he'll do something radical like declaring a daughter as his heir...
He really can't do that. While woman could be surprisingly powerful amongst the Ottomans.
Normally I'd say yes, but this is one of those situations where the normal rules could be tossed out the window, like how Maria Theresa inherited the Austrian throne in RL.
Granted she had to fight for said inheritance... Which could happen here if Selim decides to declare a daughter/sister/etc. his heir if he can't sire a new son.