ADB does not detect my device while in Recovery Mode
Considering you're using CWM (which isn't developed in a fast pace), you could switch to using TWRP, boot into recovery, enable MTP, and simply mount your internal storage or external sd card.

Copy whatever files you want onto whichever location of your choice. Unmount and flash. As I mentioned earlier, I will recommend you wipe-wipe-totally-clean-everything before re-installing. You don't want any traces of anything lingering around to hunt you!

Considering the above step worked for you, this point might not be helpful in your case, but to someone. If after everything above, supersu continues to give problems, perhaps its unstable with your phone/CM yet, and you might want to either get an updated version, or find a similar app that's stable with your ROM.