No, she didn't hear that in the show (they changed the wording to be much more vague).

This 100% won't happen in the books.

They were guilty of treason.

Regarding the Arya/Littlefinger stuff, why wasn't she using her Faceless Man powers when following him around?

Basically that everything was alright and that Robb and Catelyn should come to King's Landing to sort out of the situation with Ned's treason.

It's the letter Sansa wrote at Cersei's behest in Season 1 Episode 8.

She sucked at following people in Braavos too. Remember that hilarious bit where she followed Meryn Trant around with her little cart clacking the whole time?

Lord Glover Political Position Chart

No, I believe it belongs to his sister Talla now. Sam can't inherit anything.

Jaime mooned him from across the river before making his escape.

It's not a good play, because it would only work if Arya didn't have two brain cells to rub together. Now granted, the writers seem to be going that route.

He had main cast billing in Season 3, actually, before leaving the series entirely.

On the contrary, I'd say it's pretty clear from her reaction she bought it hook, line and sinker.

That's the letter Cersei convinced Sansa to write back in Season 1 Episode 8.

His brother was a nice guy. Sam liked him.

Which, to be clear, is totally meaningless, and Arya should be smart enough to know that, seeing as she literally spent some months on the show bringing Tywin Lannister his food.

Gendry! The prodigal blacksmith returns. I always enjoyed Joe Dempsie as part of the cast, so it’s nice to have him back. But him and Jon bonding over each other’s fathers was bullshit; Gendry saw Ned for like two minutes. If he met Arya’s brother, he would be asking about Arya.

The Dothraki punched through the wall on their own in numerous places.

If she accepted Jon as her equal, she has no real basis for conquering any part of the Seven Kingdoms.

No, the dragons died because the maesters poisoned them.