---"What is rationality/logic?
Logic is many things because there are many forms of logic. But in general, logic is essentially formal methods of reasoning by which we try to remove contradictions from our thinking.
Rationality is much harder to pin down because it tends to connote not only that which is logical, but that which is "sound" or which corresponds to a supposed "reality."
That, of course, gets you into lots of sticky areas ("truth," "reality," Knowledge" etc.) In a nutshell I would generally align "rationality" with the widely understood criteria for "knowledge:" A belief is rational when it is a "Justified, true belief." (Gettier problems notwithstanding...and I don't want to get too far into this because I'll spill too many pixels). However, I think it's important to point out that rationality need not necessarily need the "truth" quotient. In fact, it often doesn't. Mankind has often come to logical, reasonable conclusions about the world that have turned out to be wrong. But new information changed the equation and gave new insight into our error. So you can be rational but wrong (your conclusion does not correspond with reality). And, a very, very important point is that absolute certainty is not required for rationality - you can be rational while being uncertain. That may seem to contradict the idea that rationality aligns with "justified true belief." But I add in true because
it is often assumed as a component for rational action. We may be wrong in our reasoning, but when we reason on what action to take we typically do so in the hopes our ideas are corresponding with "reality."
That is really compressed and I haven't connected all the dots (like I have at length with people on other forums)...but I'll have to leave it at that for now, as a snapshot of my thoughts on the subject. (I shouldn't say "my" thoughts really, as it's all been thought before).
---" Do you take rationality/logic as thought processes which were selected for their survival value?
Yes and no. Yes reason in general arose for it's survival value. And we were thinking "logically" (at least in the classical logic sense) before logic systems were formalized. But also, thinking along these lines, our mental modelling of the world would not only be "about" the world but it would be "of" the world. In other words the world has certain deterministic laws which provides for the operation for it's inhabitants, while also placing constraints on those inhabitants. If there is a certain "reason" to the laws of nature then we must to some degree mirror those laws in our actions and to a degree our thinking. (The qualifications I'm making are important, but those might come out later). Otherwise we simply wouldn't/couldn't be here. So a certain measure of rationality/logic is necessary for the fact of our existence, not merely our "survival." (You might say, for instance, that our skin cells are explicable in terms of some logical rules that they are "following.")
---"If so, is it rational/logical because it increases survival, or does it increase survival because it's rational/logical?
Can be part of both, depending on what angle you examine. If we are correct in that our logic somehow mirrors the way the world "works" (at least at the macro level we live in) then one simply couldn't be here and not to some degree be "logical." One may take an epistemological stance, as I have before, that the fundamental (but not only) purpose of knowledge is it's survival value. In other words: To live we must act. To act we must know how to act. To know how to act we must understand the nature of ourselves and the world. So from that perspective something is rational/reasonable if it confers an understanding of the nature of the world, which in turn enhances our ability to survive.