How many papers per week does a professor typically read?
There is no typical, even within a field, because different professors tend to find different "niches" in how they relate to the literature, and the depth with which they read papers.

I have known some professors who establish themselves as the "scholars" of a department and deeply read dozens of papers per week.  I have known other professors who rarely read anything, because they focus on construction of new gizmos instead, pick up their knowledge of the field through conferences, and make their collaborators and postdocs fill in the "related work" section of their papers.

Likewise, it's a mistake to think that "read a paper" has a single definition. At one extreme, sometimes one wants to spend a great deal of time working through the contents of a paper. At the other extreme there are times one just wants to check the "headline" conclusion and see if it can help you with your problem or not.

Bottom line: there is no good answer to your question besides "it depends".