sometimes you can see if it is singular or plural only by article or adjective in front of the noun or by following verb.. you have to know particular noun. in this case. singular is "der Lehrer trinkt" and plural is "die Lehrer trinken"

also when it says Die in front of Lehrer you know its plural

"Professors" in german is "Professoren." It's a different word.

Not all teachers are professors (and not all professors, at least in the US, have teaching as part of their responsibilities;) "teacher" and "professor" are two distinctly different concepts.

I think the former is a male teacher and the latter a female