Ford Windstar 2003;3.8L engine, front wheel. Automatic transmission.

I really want to find out whether my ford windstar 2003;3.8L engine, has an engine number.I've searched all over but I can't find any. Heres my VIN:2FMZA51453BB54768.I'd really appreciate if you can help me search the internet cause i've searched on ford windstar 2003 engines and I still cant figure it out.
also;i changed my alternator, cause the wasnt able to charge the battery. The new one can now charge the battery but whenever the car is on, the alternator, gets very hot and the battery indicator lamp on the dash board wouldnt go off as required. What might be wrong with it and how can I fix it up?