I have an old(Heavy Metal) Lionel Engine and I have several questions.
Where can I find Model and Serial numbers? Can the engine be tested to see if it's worth trying to find a replacement transformer? Is there some procedure to follow BEFORE applying any power to the engine to avoid possible damage as it ha been sitting idle for many years? Where can one find replacement transformers?
First, be aware that reconditioning an old Lionel engine is not a job for the amateur. If you value this engine, and want to run it again, I recommend you find a dealer/repair shop and make the hard choice of deciding whether it's worth the price of professional TLC. Search on "Lionel trains repair shops".
That being said, I'll answer your questions, based on my experience.
The engine number itself (on the cab) is usually the model number. Look on the underside as well, you should see a Lionel tag.
Check the wheel arrangement, eg, if it has two small wheels at the front, then 6 driving wheels, then 2 small wheels at the back, it's a
2-6-2. Search on "Lionel 2-6-2 locomotive images" and you should be able to identify the engine.
If the engine is really old, the driving wheels (and the body, too) may well have deteriorated. The zinc alloy used for diecasting may crystallise over time, and the casting will break or crumble, so be prepared to replace the wheels. Also, the insulation on the wiring becomes brittle, solder joints oxidise and break, oil become varnish, and so on. Take the body off, and examine the mechanism as closely as you can. If your are unsure about your ability to clean and repair, stop, send the loco to a repair shop.
Check all the wiring, there should be no loose wires. If there are, and you are sure you can figure out where they should go, make notes so you can resolder the wires after cleaning. If you aren't sure about repairing the wiring, I'd strongly recommend you stop right there and use a repair shop.
To clean off the gunk, slosh the parts around in a degreasing cleaner. You can use a soft tooth brush to scrub, gently. Then wash them in dish detergent, use the soft toothbrush again. Let dry thoroughly. You may have to do this several times. When done, put a drop or two of light oil on all bearings, and turn the mechanism carefully by hand until it loosens up. Reassemble, and put it on the track.