2) I agree that algorithms are important, to the extent that you know the importance of "use a hash table." I don't think being able to implement quicksort on a white board is important.
They want to see your thought process as you tackle an unfamiliar problem. Do you think about the input and the end-goals explicitly? Do you consider multiple different ways of solving it, and cover pros/cons? Do you consider where issues may occur, and attempt to mitigate them? That's what they want to see.
I guess I could go dig up my old data structures and algorithms book that I haven't touched in 15 years to refresh my memory, but I don't want to work at Google badly enough to bother with that.