bran stark overdrive

It's a shame Varys had to die before Jon could teach him the secret to instantly growing a pair of balls.

The AA/TPTWP prophecy was written in High Valyrian, which is gender neutral, so "prince" could be referring to either male or female.

Beric's great mission was to save Azor Ahai Reborn during the War for the Dawn - seems like a pretty fitting and noble end for a R'hllor worshipper.

Yes, Arya is Azor Ahai/TPTWP. It was subtly confirmed by Melisandre throughout the episode, beside the fact that Arya killed the Night King with a Valyrian steel weapon, thus fulfilling the prophecy. Melisandre knew it the moment she saw Arya on the rampart. She knew it when Beric died saving Arya ("the Lord of Light brought him back for a purpose, that purpose is now fulfilled") and she knew it when she came face to face with Arya- "green eyes, brown eyes, *blue eyes*" (blue eyes referring to NK) was Melisandre telling Arya who she was, immediately afterward Arya went straight for NK. Melisandre killed herself because her purpose (finding and assisting Azor Ahai) was fulfilled, albiet at the last possible moment.