Learn Farsi: کاش پروفسور احمدی در ایران زندگی می‌کرد. - I wish Professor Ahmadi was living in Iran.

Grammatically, yes. Titles that precede a name are linked to it using the Explanatory Ezafe (porofosor-e ahmadi). However, in everyday speech, it is very common for native speakers to drop the spoken ezafe after certain Western loanword titles like پروفسور (porofosor) or دکتر (doktor), simply saying porofosor ahmadi. For native titles like آقا (âghâ) or خانم (khânom), the ezafe is strictly kept and always pronounced (âghâ-ye ahmadi).

Since Professor Ahmadi is a respected figure, shouldn't the verb be in the plural form?

You definitely can, and often should, use the plural verb زندگی می‌کردند (zendegi mikardand) to show formal respect to someone with a high-ranking title. The singular verb زندگی می‌کرد (zendegi mikard) used here is grammatically correct but implies the speaker is talking in a more casual, everyday tone, or perhaps knows the professor personally.

Why is the verb زندگی می‌کرد (past continuous) used when wishing for something to be true right now?

The word کاش (kâsh - I wish) introduces an unreal or counterfactual statement. When you wish for something contrary to present reality (he doesn't live in Iran, but you wish he did), Farsi uses the past continuous tense. This is very similar to English, where we also shift to a past tense ("I wish he was living in Iran") to show that the situation is hypothetical.

Could I use the native Persian word استاد (ostâd) instead of (porofosor) here?