The oil in the coolant usually indicates a leak in your oil cooler. Oil pressure in the engine is higher than the pressure maintained in the cooling system so oil get forced through the leak in the cooler into your coolant. The A/C not working is totally unrelated. I would generally agree with your mechanic that the pressure switch on the compressor is defective and not triggering the auxillary fan to come on. It would be best to have your error codes scanned first though before buying parts you may not need.

2002 X5 3.0 303,700 miles
2014 428i 19,000 miles

2004 325i sold at 123,600 miles
2001 325i sold at 66,000 miles

1970 Firebird - undergoing restoration