Can I put a 92 Buick Regal Motor into an 01 Impala?

Nope, the 93 model is OBD I but the 02 model is OBD II. They're completely different computer control systems and are not compatible with each other at all! Hope that helps! Jim

Try to determine if it is engine oil or transmission oil in the coolant. If it is ATF he just needs a new radiator assuming the transmission is not contaminated with coolant.

Definitely check what F_O_R said. If it is engine oil and has the 3.8L V6 he most likely needs the intake manifold gaskets done. Inspect the top of the engine and look for coolant or oil pooling on top of the lower intake manifold under the plastic upper intake manifold. If that's the case, when you do the job replace the upper intake manifold, don't reuse it. They always crack. Use the FelPro second design problem solver gasket set. If the lower intake manifold needs to be replaced don't buy the Dorman lower intake manifold. It won't fit properly. Most times that lower intake manifold can be reused though. After the repair change the oil twice to be sure any coolant that got into the engine is gone. If it has the 3.4L V6 it's most likely a blown head gasket and the vehicle is not worth fixing. Keep in mind that these vehicles are also notorious for transmission problems. They lose overdrive and TCC lock in resulting in the transmission not up shifting to overdrive and killing your gas mileage. That's about a $1,500 repair at a shop. I'm guessing that since it hasn't been overheating it's either what F_O_R said or the 3.8L with the common intake manifold gasket failure. Hope that helps! Jim