Arya´s Creed

I have got 3 questions as well. Hope you can help me out.   1. Cersei was married to Robby B. so why is and was she called Cercei Lannister all the time? Shouldn´t it be Cercei Baratheon?   2. Everyone says that the R+ L theory is so important because if it is true then their son would have a claim to the throne, even more so than Dany. But I think neither would have a claim since Robert won his rebellion fair and square right? So not the past kings but  Robert´s descendants should be the heir, right? But he has no trueborn kids so Gendry is the one true king? I´m so confused  :stillsick:   3. When I think about everything that happend after Robert became King, I see that f*cking Littlefinger is reason for every tragedy that happend (especially to the Starks). He needed Ned out of the way so he could marry Cat, so he killed Jon Arryn because he knew Robert would make Ned the Hand. Once Ned was in Kings Landing.... well you know how it went on. But I can´t see the big picture. What is his plan? He can´t be the king. If he wanted to be Warden of the North, he would´ve married Sansa himself, but then Cersei would kill him. What the f does he want man  :drunk: I know he once said to Varys that Chaos is like a ladder for him. But how far does he think he can climb this ladder?