Prof Doe in/at the Department of, in/at the Faculty of, at/in the University of [duplicate]

I like your version better than your editor’s. In particular I dislike “at the Faculty”— unlike a University, a Faculty doesn't serve double duty as both an institution and a place. The Department is a group of people within a larger group of people who are all at the place.

(In US usage, Prof Doe is on the Faculty; but here the syntax implies that it is the Department which is related to the Faculty.)

However, I suggest one change: Prof Doe of the Department ... Being in the Department suggests that Prof Doe is merely a minor piece, a cog in the machine—which of course may be the case, but if so should not be acknowledged. Of the Department sounds much grander, like Arnold of Rugby or Lawrence of Arabia—the illustrious Prof Doe, distinguishable from other Profs Doe, unknown and unsung.

(But if his title is grander, this would not be appropriate; you postpose the title:

John Doe, Egregious Professor of Whatsis in the Department of Whosis, Faculty of Whatever at the University of Wherever.)

There are many meanings and uses for both of these prepositions, some logical, some idiomatic.

In the uses you ask about, I think the following meanings are most helpful

The first meaning in the COED for in is

expressing the situation of something that is or appears to be enclosed or surrounded by something else:

In that same reference, at is defined as

expressing location or arrival in a particular place or position:

Both in and at are used to denote location, and the choice of which may be logical, but is often idiomatic. In the street but at the corner of Hollywood and Vine.

However in can be used non-geographically to convey being a part of something (in an organization), as well as literally in the middle of something (in a crowd). The preposition at is much more specifically physically locational (although it has other meanings relating to time and measurement).

In your examples, Department and Faculty convey a group or organization of which the subject is a part, rather than a physical location. As such,when used with Faculty, in seems better, and at would jar (at least in US usage). Department is a bit less clear, perhaps because it is often associated with a particular location. Either could be used, but I think in would be strongly favored, again in US usage.

He works in the Department of Defense [yes].
He works at the Department of Defense [yes].
He works in the History Department [yes].
He works at the History Department [perhaps].
He is enrolled at the History Department [no].

University, on the other hand, is both an organization and a physical place. While both in and at seem correct, I would probably favor at, if for no other reason than avoiding repetition.

"In the faculty" is correct usage.

Both "at the department" and "in the department" are valid.

"at the University" is the correct usage.