Rather than memorizing stuff forever, you could develop your intuitions about data structure design trade-offs and what makes them behave the ways they do. After I learned OCaml, a lot of data structure design seemed obvious.
Also, read _Purely Functional Data Structures_ by Chris Okasaki. Unlike (say) CLRS (http://mitpress.mit.edu/algorithms/), it's even a pretty short book.
Exactly. The OP thinks that when I ask her to reverse a linked list, I expect her to whip out the perfect code from memory on the fly. I would be even more suspicious if you did that actually. I want you to structure the data. I want you to try out variants of reversing. It is ok if you can't give me the optimal solution in 5 minutes, as long as you demonstrate the capability to reason with data structures and pointers and tools at hand.
I'd actually recommend not reading Chris's book in isolation. There are a lot of things that are ugly to do in functional languages (w/ respect to data structures), but are easy with assignment (and of course vice-versa). I'd read Chris's book with Sedgewick (Sedgewick is a super applied algorithms text). This will help give a good balance.
I partially suggested it because it uses SML for the code. Even if one doesn't use OCaml / SML for actual programming, using the notation will probably help quite a bit with reasoning about data structures.
Also, read _Purely Functional Data Structures_ by Chris Okasaki. Unlike (say) CLRS (http://mitpress.mit.edu/algorithms/), it's even a pretty short book.