For the episode on Night's King:
It's worth to mention that The World Book makes note of Brandon of the Bloody Blade as an ancestor or father of Brandon the Builder, while being a son of Garth Greenhand himself. There is little known about him, except the very vague and minimal mention of his exploit(s) towards the giants and the Children of the Forest. However, these do seem quite significant and have a direct link to the notion of Stark justice and the swinging of the sword as we learned from Ned.
That there is little mention might also be seen as significant on it's own in relation to the tale of Night's King and his statute of 'being erased'. But also Old Nan's points out that Night's King is from the Stark family, and Brandon of the Bloody Blade being the father of Brandon The Builder might be very explanatory since Old Nan wouldn't be really telling a lie, but rather a bit of a muddled truth. There is a connection in the bloodline, although the real Night's King might have predated the actual foundation of House Stark. (although other stories tell it might be a Flint or another family... which could also be explained as Brandon of the Bloody Blade being a common ancestor of the Starks, Flints, and a lot of the early Houses of the North)
This Brandon of the Bloody Blade, might also be the one that is referred to in ASoS, Bran III when another Brandon than Brandon The Builder is being distinguised by some maesters as the Brandon who 'Brandon's Gift' stems from. If Brandon of the Bloody Blade is actually Night's King, it wouldn't be so weird that there is lots of confusion between him and his son as the Brandon from whom 'Brandon's Gift' originated since Night's King is supposed to be struck from history books and forgotten.
Another interesting similarity (of numbers) is that the story of the Last Hero mentions that the hero had a dozen compagnons, while Garth Greenhand had 13 children (which could stand for 12 children and a hero, as well as the 12 commanders of the Night's watch and a fearless hero)
Night's King (and the Last Hero) might in this way maybe not so mutually exclusive, but can very well be and extension of one another: the same story told different, but heavily muddied through oral tradition, so there is no apparant link. The might very well both be part of the tales of the origin of mankind (as the westerosi, or the Houses in the North could be descendants of this 'unholy union' too, or the union might also be exactly what saved them -a pact of sorts-)