I've found http://www.ccs.neu.edu/home/matthias/HtDP2e/ to be the best resource to drill the "code as data" mindset necessary for Lisp programming. And I would recommend going through as many exercises in http://sarabander.github.io/sicp/ as possible using the Racket IDE: https://docs.racket-lang.org/sicp-manual/index.html

either or, Clojure has more of a focus on functional programming and immutability than some other lisp implementations but honestly they don't really get in the way and most lisp lean that way anyways. Personally I would say stick to Clojure or CL as there is a wealth of information and libs available for those two. Others will differ but once you know one it's a matter of style and conventions to adopt a different implementation (until you get under the hood)

There's really no need. Most of the Clojure material out there doesn't assume or require Lisp knowledge. Unless you're interested in specifically learning Lisp, of course.