Around 2nd episode of the 4th season. When gifts are presented to Joffrey (Tyrion gifts a book, Mace Tyrell a cup and Tywin the Valyrian steel sword that Joffrey names "widow's wail") Cersei says to Tywin that Shae is Tyrion's whore. The scene where maid tells on Shae is in the episode when Jaime gets his golden hand. Qyburn leaves the room after Jaime comically waves him off,Jamie and Cersei are talking, the maid knocks on the door to Cersei's chamber, Jaime was horny so he shouts "go away" while Cersei let's her in. The maid sees when Shae runs out after Tyrion does the "you are a whore" speech to Shae.
At this stage Bran only has fragments, he said so in the last episode. Sansa knows of Lysa's death as well as the things Lysa was saying (poisoning of Jon Arryn, sending the message to Catelyn) but no direct knowledge of his anti-Stark deeds. Arya was Tywin's cupbearer when Littlefinger visited Harrenhal. Arya and Sansa will urge Bran to take a closer look at Littlefinger and that will be his undoing.
Yes, he has been burned in the show. When the two wights tried to kill Jeor Mormont (old commander of the NW) Jon burned his hand as he threw the lantern at one of them. The commander dispatched Alliser Thorne to take the dead wight's hand to King's Landing but the show never followed up on that.
...then they'll have to say that being resurrected enabled it somehow or something. Like, maybe his Stark side was killed off or the Lord of Light revival unlocked his Targ abilities.
Went ahead and made an outline for several more episodes if they do go that direction. I'm sure I'm way off!
Last episode of GoT:
Bran told Sansa that he needs to speak to Jon. Danny's aides tell her that it's too risky to let her fly a dragon into battle. Lady Tyrell tells Jaime that she killed Joffrey.
Next episode:
Bran tells Jon that he's actually a Targaryen. Jon doesn't believe him. Bran offers his services as a Dragon Rider using his warg abilities. Jaime tells Cersei about the Tyrells admitting to killing Joffrey. Cersei still hates Tyrian for siding against her with Danny.
Next episode:
Bran shows Jon the truth by warging in or whatever. Jon realizes that he really is a Targaryen. He tries to tell Danny but she interprets it as a false claim to the throne and orders his execution by dragonfire. Cersei does something horrible and Jaime begins to realize that she is as mad as The Mad King before her. His love for her diminishes. It already felt like a contradiction that he would support her after turning on The Mad King when he was explaining to Lady Tyrell how Cersei wanted her killed.
Next episode:
Jon's Targaryen blood protects him and his fireproof hair turns blonde during the execution attempt. People witness Jon going Super Saiyan and everyone, including Danny, realizes the truth. Jaime defies Cersei's attempts to kill Tyrian putting him into direct conflict. He has to make a choice much like when he chose to end the rule of The Mad King.
Next episode:
Still having no desire for power, Jon defers rule to Danny. He and Bran each command a dragon into battle in the north. Danny, needing to prove that she is more than just a throne room ruler, also rides into battle... and dies. With Jaime's betrayal, all Westerosi houses are allied against the white walkers and The Night King.
Next episode:
Battle ensues. Harsh winter. Yadda yadda yadda. Jon
Snow [Targaryen] ends up on The Iron Throne. King of the North. King of the Seven Kingdoms. King over Danny's parts of Essos. Still having no desire for power, Jon forms a representative democracy involving the seven Westeros states, Dothraki, and Danny's other Essos lands and they all live happily ever after.
That's my outline. Let's see how it goes.