welcome....
there is a switch located in the plastic cover of the wiper motor gearing case witch can go faulty and cause a loss in wiper motor functions either intermitent or casuing the wipers to stop anyware on the screan or total loss of wipers
somtimes this is casused by the switch overheating when the wipers have been used on a frozen screen and forced across it.
as for the rough idle it could be the idle control valve as said