I would not recommend bringing a written list of questions
You should aim as much as possible to ask personalised questions to your interviewers, not generic questions about the firm/office. For example, if the interviewer bio (if provided) says the interviewer did an externship somewhere, ask them about that.
Treat this as a time to really get to know the people who work at the firm. Your interviewer won't be excited after 6-10 hours of interviews in a day to answer your questions about the office/company - people are much more likely to get excited about talking about themselves.
Only ask a question about the firm if it is really something you want to know and cannot find an answer online/by speaking to people at other events/etc. It will actually reflect poorly on you if you ask a series of questions that could have been answered by looking at the company's website / a google search. If it is something you really want to know the answer to, you shouldn't have to write it down to remember what it is (to your point about forgetting questions)
Finally, you are not being assessed on what/how many questions you ask. An interviewer would much prefer a few questions that relate to them personally than a list of pre-prepared questions.
Don't stress about this - there are much more important things you should be thinking about before your interviews than the questions at the end!