have the heater core checked and the first thing you should check is your radiator fluid to water ratio with a berometer there like 5 bucks at an auto store
Check coolant in radiator could be getting mixed with transmission fluid due to a bad radiator cooling chamber Check the modulator could be getting burned as fuel Check for leak
The 2005 and up Mustangs don't have dipsticks Ford considered sealed so it shouldn't need fluid unless it has a leak.
Check your brake fluid level.
Check the manual. Full diagrams of 2005 engines and locations of parts.
Take the radiator cap off when it is cold and check the fluid level. Just because the recovery tank is full does NOT mean that the radiator is.
DOT ( 3 ) brake fluid ( according to the 2005 Ford Taurus Owner Guide )
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Milky means that there is water in the fluid. You need to have the radiator checked for an internal leak.