do a 2002-hyundia elantra 2.0 liter have a timing belt.
Yes. replacement is at 60,000 miles
Yes, your Hyundai Elantra has a timing belt, and the engine is of the “interference” type.
This means that when the belt snaps (without any warning lights or sounds, or prior changes in performance), major internal engine damage will take place.
Incidentally, the Hyundai Maintenance Schedule that should be in your glove compartment mentions timing belt replacement as one of the vital maintenance procedures that this car needs periodically. It would be a REALLY good idea to start referring to that maintenance schedule before you have major problems caused by lack of maintenance.