About fast scrolling. It is already there. Try scrolling on the right side of the display. the fast scroll area is rather small to not colide with album/artist grid view elements.
About the artwork issue I'll have a look.
Searches are not stored locally. I don't think this is possible because I can't check if search results would have changed without getting the actual result from server, I think. I could try to optimize the result fetching a bit, maybe.