I could see a case for Tywin as either INTJ or ENTJ, but I think that his Ni is more dominant because all of his actions are guided by a singular, uncompromising, personalized vision of making House Lannister the sole ruling power in Westeros. There is no doubt in my mind that Tywin uses Te in his functional stack and I would say that it is only slightly subordinate to his Ni, making both INTJ and ENTJ equally plausible. However, he also tends to chide his children for being rash and impulsive, which to me suggests a case of inferior Se, albeit a well-developed Se, but nonetheless inferior.
I do think Littlefinger is an INTJ masquerading as an ENTP, but I think he just does it so well that even us, as viewers, can't help but to sometimes fall into his coaxing trap.
Daenerys' actions are all based on her internal sense of ethics. For example, when she decides to put all the former slave-masters to death, she remained adamant and insistent on doing so against the advice of others.
I would like to clarify something here. I do not want to play on the stereotype that ISTJs are dutiful and traditionalists. Additionally, I have seen compelling cases for Jon Snow being a few different types. That being said, I think that Jon is a dominant Si-user for a few reasons. As a bastard, he seems to have accepted this role of his in society and doesn't try to fight against it or prove otherwise (inferior Ne). Additionally, there are many situations that arise within the books and the movies in which Jon is reluctant to abandon his vows. This shows that he wants to work within a system, in contrast to FPs who want to blatantly work outside and defy systems (like Oberyn Martell, Robert Baratheon, Arya Stark, Daenerys Targaryen etc.). For example, when he says that he is reluctant to lie with a woman because he is afraid of producing another bastard child, this is an example of Jon pointing out the logical consequences of what would happen if he were to take a certain sort of action (Te). I don't think that Jon is a dominant or auxiliary Fi user of any sort, because he is able to overcome his personal emotions in most situations to make rational decisions, although I think that his thinking and feeling processes are very much closely linked together, in contrast to someone who is an IxFP.
As for Catelyn, well, that judgment was based more on a vibe, tbh. I didn't really care enough to analyze her that much.