If I have taken medication, how long should I wait before lying down? I ask this in order to avoid damaging my esophageal sphincter. I guess that the same question also applies to after eating food.

Do you suffer from Acid Reflux Disease?
If you are healthy, most people can lay down immediately after eating and such, as the function of the sphincter is to contain these things in the stomach.
If you suffer from acid reflux, you may want to experiment as the time will vary from person to person; as a general rule, 2-4 hours to allow the stomach to empty would be advisable. Alcohol and certain medications (narcotics, tranquilizers, etc.) would have course slow down this process and/or serve to relax the sphincter so you would want to wait longer than normal.