Translation:Many professors teach in the university.
Should be "the professors instruct" not "the professors instructs." However, I find that "the professors instruct" isn't accepted either, so I'll report it.
However, "teach" is really a better choice here than "instruct." "Teach," includes all the things a teacher does -- grade papers, plan courses, research material for courses, as well as classroom and one-on-one instruction. "Instruct" (laŭ mi) means when the teacher works directly with the students to give them information. I'm a native English speaker from New England.
A homonym is a word that sounds the same but means something else. For example "boy" and "bouy" (at least in UK English - American English often pronounces "bouy" as "boo-ey"). I think that you meant synonyms.
In the UK, universities have professors and lecturers. Back in my university days neither group would claim to teach. They would lecture and expect you to teach yourself. So professors and lecturers were not teachers, but they might be now. Back in those days, very few of the professors even lectured, so it would definitely not be true to say that many professors taught in the university,