Are you sure it is oil residue? If it is dark brown or reddish brown is is probably long life coolant residue. Typically coolant can be forced into oil from a failure of a sort, but not the other way around from what I have seen. Transmission coolers have been known to rupture inside the radiator allowing the two to mix. Your transmission fluid gets a stawberry milkshake look to it. But I don't recommend drinking it no matter good it looks. But this condition will wipe out a transmission if not caught early on.
There are plenty of ways a car can break down without the radiator being a part of the cause. As for the reason you'd see steam from a radiator, it would escape if there was a leak in the radiator or the hoses, or if the cap was opened. The contents in a radiator are very hot - hot enough to produce steam.
Lower radiator hoses in water cooled engines are return lines. The upper radiator hoses are feed lines of hot engine water to the radiator. The reason that lower hoses are cooler is that the radiator has allowed much of the water's heat to dissipate into the air. Thus, a lower radiator hose contains cooler water than other radiator and heater hose lines.
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