Rebuttal is limited to 500 words, but the reviewers asked almost 20 questions
I suspect I know which conference you are talking about (I am in the Program Committee) :)

Answering questions in the rebuttal phase of conferences is a newly emerging skill. Almost any paper faces the issue that you are facing - rebuttals are strictly word-limited, and the reviews / questions are waaaaay too long to clarify everything.

A good strategy for dealing with this depends on you understanding how the rebuttal will actually be used in the final phase of reviewing. Essentially, after your rebuttal, there will be a final phase of (online or physical) discussion among the reviewers and PC chairs to decide if the merits of your paper outweight its limitations, if the paper is important enough to warrant presentation at the conference, and so on. Many papers have nobody really willing to fight for it (i.e., everybody mostly sees limitations), and for these papers your rebuttal will not change anything. A handful of papers will only have people positive about the work, and in these rather rare cases the paper will be accepted no matter what you write. Some papers will have one or more quite positive people ("champions") and one or more people who are sceptical or downright negative. In these cases your rebuttal can play a major role in how the discussion goes.

Your rebuttal should be written for this specific case, and it should be written to give the champion(s) the best possible ammunition to counter the arguments of the sceptical crowd. That means:


Answer questions where you have a really convincing answer, especially if they come from the most positive reviewers.
If you identify factual mistakes or misunderstandings, clarify them directly and without the polite hollering one tends to do during journal reviews.
Focus on questions or concerns that multiple reviewers have, especially if you have a good argument.
Focus on concerns regarding methodology, validity, or importance of the work. Don't focus on presentation-level issues (the champion can always make an argument that these can be fixed in the camera-ready version, you don't have to point this out).
Remember that you don't get an actual revision for most conferences. Do not agree that some additional work will be needed (even if it's small), this will work against you.
Do not get into discussions that are a matter of taste or subjectivity (you won't change anybody's mind on those).
Do not feel like you need to address everything.
Skip polite phraseology ("Dear Reviewers, we are very grateful that you took the time to ..."). Get to the point.


Importantly, it's not similar to a response letter for a journal. You do not have to convince every single reviewer. Counter-intuitively, you need to focus your attention on the reviewers that may fight for your paper, and the ones that could realistically change their mind (in that order). Don't worry too much about a single reviewer that will never love your paper (especially one that does not like the kind of work you do or doesn't think it's important). You won't change their mind, and if the others champion your paper the PC chairs will likely side with the positive reviewers. Whereas in a response letter you will often "agree" with certain reviewer comments and fix them in the revision (even if you don't really agree), your goal here is to convince at least a subset of the reviewers that your current version is good as it is. Agreeing with the reviewer's concern may or may not get you sympathy points, but it will definitely not help you get the paper accepted.