First let me say that I have a lot of experience with math department admissions, all of it in a department which is separate from the statistics department. The title question is "Constructing a mathematics CV": I'll answer that. I would not assume that it's the same for statistics.
For a math admission -- either master's or PhD, it doesn't matter -- the CV is just about the least important part of the application that I can think of. At many places, it is probably being asked for as much out of force of habit as anything else: in academia, CV's are ubiquitous. However, most information that is provided on your CV is also provided elsewhere on the application: grades, coursework, research experiences, relevant personal experiences all have other outlets. I can only remember reaching for a candidate's CV when something was missing from some other part of the application (possibly because of a clerical error on our part) and I wanted to quickly put my hands on it. I absolutely don't care how the CV looks, how it is formatted, or anything like that. In fact I don't care about that stuff for any level of academic job. And in fact I myself have one of the more unimpressively formatted CVs I've ever seen, almost to the point of being unintentionally "unbusinesslike".
So I would say the key is this: whenever you're wondering whether to put something on your CV, also ask yourself: "If I do put it on my CV, how do I highlight it elsewhere in my application?" Because your CV might not even be specifically read by some (or all) committee members.
To answer your specific questions:
if I volunteered as a TA, should I throw this experience in teaching instead if I don't have any other volunteering experience?
You should certainly include all TA experience, volunteer or otherwise. (Whenever you do something as a volunteer that one might reasonably think you've been paid for, it is only honorable to clarify that you were a volunteer.) I find your concern that you don't have any other kind of volunteer experience misplaced: we're not looking for volunteer experience, and volunteer experience that is not math related is not clearly relevant at all and should probably only be included if it is truly notable or substantial. Honestly, we're not selecting for candidates who are unusually socially conscious or unusually well-rounded, so your volunteer work would have to be successful enough to show exceptional drive and/or administrative skill.
Am I missing anything?
No, I don't think so. Your research experience -- if you have any -- is one of the more important things to go on a CV, and you mentioned it. But in keeping with what I said before, it is really too important to just hide in a CV: if you had any research experience at all you should certainly mention it in your personal statement (and if you haven't had any at all, it would be a good idea to address that, at least by saying how excited you are and how much you welcome the opportunity). If your research experiences resulted in actual product, then include the product itself: papers can be part of the application, and you can also include links to websites.
how much detail am I expected to put in for my experiences? Am I expected to talk about "excellent communication skills" or "teamwork" in any of my experiences, if applicable?
At this point I wonder if you're confusing the CV and the personal statement. You don't "talk about" anything in a CV: it just displays information. There is not a single complete sentence in my (eight page: yours should probably be one or two) CV. Information about relevant experiences should go prominently in your personal statement and you should do what you can to ensure that these experiences are also discussed in your recommendation letters (along with your coursework, these are the most important part of the application). I have no desire to hear about excellent communication skills or teamwork from the candidate herself, no. In fact, writing a personal statement that is literate and moderately compelling is your big chance to show your communication skills. Openly boasting about skills is something that academia largely frowns upon. This can get tricky when in certain contexts -- grant applications, introductions to papers -- you really need to describe your achievements, but in a way which is factual and not openly self-promotional. In a grad school application I would strive to look competent, eager and (reasonably) humble.
are there any online forums where I can get feedback on my CV (mathematics-specific would be extremely nice)?
You should ask your recommenders for feedback on your CV. They are natural candidates, because (i) they're reading it anyway and (ii) they have already shown an interest in your academic career. The right way to do this is to first give them a CV and make it really clear that you want critical comments and that you've saved plenty of time for it -- more than a month! -- and then after that you would like a recommendation letter.