The pedal that you referenced only has two wires coming out of it (its a mono jack thus two wires). I think the "polarity switch" they refer to changes the switch contacts from normally open to normally closed (as that is the only thing that will work with only 2 wires) thus one direction or the other of the "polarity" switch will be the same as your current switches. As to how perf board works if you get one that is the same as the breadboard, there are two strips of copper horizontal (the two power busses) then 5 hole strips vertical (the 5 vertical connections on the breadboard a space another 5 vertical connections then 2 more horizontal power strips. you solder the components to the perf board the same way they connect to the breadboard but instead of plugging them in to the breadboard you make the same connections by soldering them to the perf board. Technically you don't really need perf board. You can wire one end of the pedal to ground (all of them together just like the power connection) and the other end of the pedal to the port connection on the uno just as your switches are now and that should work. I expect a nano will have sufficient connections to drive the leds you want, but you would be best to test that on your current setup before commiting one way or the other. You may have to do some port expansion to get enough ports, but I expect you won't need the larger memory that is the main advantage of a mega (but I also may be wrong here 
). I'd try it first on the uno before committing to a mega.
Peter