I'd like to know on which questions and how much I voted. Is there such a query? It would be nice to share it.
I'm sure i've seen it mentioned specifically somewhere in here, but finding the items you voted on is not possible via the public search, or via the publicly available data dump. The main reason being that Jeff wants some badges to be a surprise (as mentioned in the link from @Filbert), and to prevent finding out who downvoted your question/answer and seeking retribution by downvoting them.
To my knowledge, this query does not exist in the regular interface. There is a dim chance you can use the Stack API though, but I'm not familiar with that. :)
For downvotes, as S.Mark proposed, you can have a look at https://stackoverflow.com/reputation - it says "3" on the left for downvotes. For instance:
[...] 2 519538 (5) 1 519557 (2) 3 123456 (-1) #this is a downvote, also displays the question number (123456) -- 2009-02-06 rep +6 = 249 #and here is the date for your convenience