there not related. The oil burning is related to rings and/or valve seals. Test the fan by hooking it directly to the battery. If it works then your fan is good and either a sensor is bad or your fan relay is bad. Also when you replaced the hoses did you bleed all of the air from the system? That will cause it to overheat also. Here is a link to a manual, will show how to bleed the air.
http://www.binghamtonlife.com/manual/2gsm/default.htm