1. Who will sit on the Iron Throne?
Your guess is as good as mine on this one. For what it's worth, I think it'll likely be Jon and Daenerys' future child.
2. Why didn’t the White Walkers attack Sam?
Honestly this question still haunts me, but the most likely explanation for Sam escaping the Walkers at the end of Season 2/beginning of Season 3 is that they didn't see him. I guess he's really good at hiding.
3. How many White Walkers are there?
We don't know. But we do know Craster sacrificed 99 sons to them, so, presuming they all got turned into White Walkers...there's over 100, at least?
4. What are White Walkers?
The White Walkers are all former humans who have been turned using magic. The first White Walker, the Night King, was turned by the Children of the Forest when they inserted a dragonglass dagger into his heart. Presumably the Night King himself then created the rest of the Walkers.
5. What kills White Walkers?
Dragonglass or Valyrian steel. Although the Night King is likely different and harder to kill.
6. What do the White Walkers do with the babies?
Turn them into more White Walkers, if the scene in which we saw them turn Craster's last son is anything to go by.
7. Who is Gendry related to?
Gendry is the son of Robert Baratheon, the nephew of Stannis and Renly Baratheon, and the cousin of Shireen Baratheon. All of whom are dead. He's the last Baratheon that we know of (although he's a bastard).
8. How are Ned Stark and Robert Baratheon related?
They aren't, although they were both wards of Jon Arryn at the Eyrie so they grew up together. And Robert Baratheon was betrothed to marry Ned's sister, Lyanna – but Lyanna ran away with Rhaegar Targaryen before Robert could marry her. It's what kicked off Robert's Rebellion.
9. Are Jon Snow and Ramsay Snow related?
No. They both have the surname "Snow" because bastards aren't given their father's names like legitimate children are – they're given the bastard name of their region instead. Bastards of the North are named Snow. Of course, Jon Snow isn't a bastard of the North at all – but that was the story Ned used to protect his identity and his life. And Roose Bolton legitimises Ramsay so his surname becomes Bolton, too.
10. How is Rhaegar Targaryen related to the Mad King?
Rhaegar Targaryen was the Mad King's son and heir. The Mad King had three kids – Rhaegar, Viserys (who was killed by Khal Drogo in Season 1) and Daenerys.