For some reasons I need to know about the level of research conducted in a certain university (not because I want to study there: I got my Ph.D. years ago). Specifically, I'm interested in a certain department. I did some due diligence, such as looking at the Google Scholar profile of one of the professors, and looking at the website, but I didn't get a conclusive answer. Can I ask this question on Academia.SE?
The question you propose would be a shopping question as it asks us to evaluate an individual university. What you can ask about is how to evaluate the research level of an anonymous university (unless we already have a question on that).
Not sure what "level of research" implies, but I imagine that would not be a good question for this site, as that's fairly subjective. I can't imagine what we'd post beyond what you already were able to find for yourself.