A couple of weeks ago, I emailed a professor (at a different university) about becoming my graduate advisor. While they didn't explicitly agree to do so (the program isn't accepting new students until next year), they expressed interest in my proposed thesis topic and asked the program director about a specific disability accommodation I mentioned. They also gave me his email in case I had further questions about the logistical issues etc.
My question is: Would it be impolite not to email him or would that seem like I wasn't seriously interested in the program. (The professor answered my questions pretty thoroughly.) I've thought about asking him if they have "rolling admissions" or if it would be too early to apply within the next couple of months (currently studying for the GRE, so I can't apply before I take it), but then I thought that asking such a trivial question might be worse than not contacting him at all.
Also, should I have thanked the professor for their reply? I had even brought up the situation with my previous prof. (whom I fell out with), which most professors would probably have seen as a red flag, but they expressed understanding. Given their kindness, I didn't want to be rude by not replying, but I'm not sure how to reply. Would replying to such a thorough email with one line such as "Thank you for the information" seem curt, and is it too late since almost two weeks have passed since then?
*To clarify, this new professor knows the other professor that I had the falling-out with, so I figured I would take the chance of explaining the situation and asked them to help me reconcile with her. (If anyone is unfamiliar with the situation, I misinterpreted her [my former professor's] email and wrote a letter to the department chair accusing her of triggering my anxiety on a few occasions with a "curt" tone, but later tried to retract the grievance and wanted to apologize to her.)
Update: I emailed the director, and he sent me a friendly reply answering my questions about the deadlines etc. I genuinely was curious about the deadlines, it wasn't that I was making up an excuse to email him, but I thought it might have been a "trivial" question. I don't know how he actually perceived it, but his email was polite and welcoming. I then thanked him for the information.