Jaromir, this video shows how to reverse the orientation of a coil in the Allen-Bradley IEC-style contactor (move terminals from top to bottom), but the method to open the contactor case is fairly clear. It would be simple matter to replace the coil while it's open.
As for the loose wire, without a wiring schematic, I would be just guessing - - and would hate to steer you in the wrong direction. I'd contact the manufacturer for tech support.
Last edited by Malcolm McLeod; 01-31-2018 at 9:51 AM.
Reason: for Allen-Bradley