The show hasn't signaled that Jon is unstable, but if I were writing it, I'd throw an ominous sign or two into the mix in the last episode. I wouldn't have Jon commit any grave crimes, but I'd do just enough to give people an unsettling feeling as the show wrapped up.
Danny isn’t a Martell, because her father Aerys married his full sister, Rhaella Targaryen.
Jon’s father, Prince Rhaegar, first married Princess Elia Martell. So Jon’s half-brother and half-sister were half Martell.