I have a question. What is the etched writings and numbers on the inside of the back of the watch case. Sometimes they're number or numbers and letters and some times they are crossed out. Does watch makers/repaires engrave a code on the back? Do they have something to do with services?

You are correct on both guesses.

Well, does anyone know what the codes mean? Dates serviced? Serviced by who? Why cross the codes out?

Normally it is something for the watchmaker. His code or initials and something representing the date. The latest one MAY cross out the older ones.