"Professor" is both an honorific title and a job name, whereas "Teacher" is only a job name. This means that "Professor" can be used before a name and this is also the case with "President" and "Doctor" as you mentioned. Although it isn't wrong to call some "XXX the [job name]", it isn't commonly done. We would usually just introduce the person in the following way: ---> "This is Mike, he's a postman". As for "Mr" or "Madam", in regards to jobs, they can only be used for top ranking politicians (Mr. President or Madam Secretary etc.) and no other job; this is also almost only exclusively in America too by the way.

You're correct. Professor can be a proper title before someone's name (e.g. Professor Johnson) just like Dr. Johnson, Senator Johnson, President Johnson. However, the job titles teacher, instructor, tutor, postman, and many others are not used as a proper title with someone's name, so you would simply call him Mr. Johnson. Saying "Mr./Madam + [job title]" is reserved for only certain positions to show respect, usually a high ranking politician - Mr. Secretary (for the Secretary of State in the US), Madam President, Mr. Ambassador, etc.

Thanks Gray, learned something. Have a nice day ~

I agree with Adam. If you want to be specific about which "Mike" you're talking about, you can also say something like, "Yesterday I had a conversation with Mike, the postman." "Have you met Johnson, the teacher who lives next door?" It sounds strange to just say "Johnson, the teacher," because there are probably a lot of teachers in your area, so saying "the teacher" isn't very specific. "The postman" is okay, because we assume that you're talking about the specific postman who brings *your* mail. But for words like "writer" or "soldier," you'd need more detail. "That's Bill, the soldier I was telling you about yesterday." It would be very rare to refer to him as "Bill the soldier."