Wish there were a bit more instructions on how to get it running using lein2 / project.clj. Maybe that happens this weekend :-). I am a bit at a loss how to start the webserver used by c2 (and if its even included) from within emacs/slime/swank.

There's no webserver built into C2. The visual REPL is a separate (toy) project.

To use within Clojure, just add c2 to your deps as usual and then

    (ns your-ns
      (:use [c2.core :only [unify!]]))

Use from within ClojureScript is pretty much the same. Checkout

https://github.com/lynaghk/cassowary-cljs-demo

for a rough demo.