Cell color base on Odd/Even Week and Day criteria

I have been searching around and just cannot find a way to deal with this much less find a way to start. I have a column representing each date of the month. I would like the cells beneath to color grey as to whether the date is a Monday and is in an even week and if the code to the left of the employee is "EM" (which stands for even Monday). I would ultimately want the same for even week Mondays, odd week Fridays, etc. depending on the code beside the employee name.

I attached a spreadsheet that shows what I am trying to accomplish. Any assistance is greatly appreciated!!!