Hi Tavia12 in Toronto,
You will get slightly different responses from nearly everyone on this because there's a huge variation among surgeons about exactly how they like to do this procedure (there's generally less variability for a procedure such as breast implants).
You can, in theory, do many different areas of the body using local anesthesia alone and you can, of course, do as much as you want under general anesthesia (there are obviously limits on the amount of fat that can be removed safely at one procedure, regardless of which method is used).
My preference, though, is to use local anesthesia with intravenous sedation for the majority of the procedures I do. I cannot (in general) get as complete a result with local alone, compared with using some sedation. It doesn't have to be general anesthesia technically (ie, with an endotracheal tube - in fact, it is somewhat of a semantic issue when you start talking about exactly what constitutes general anesthesia); actually, deep sedation is pretty close to general anesthesia. Although I can remove a reasonable amount of fat from one or two areas under local alone, the difference between a good and a great result is often that extra bit - and that is best done, in my experience, using some sedation.
So for all the areas you're talking about, I would probably advise using local anesthesia with intravenous sedation for the best likelihood of obtaining the result you (most likely) want.
I hope that this helps, and good luck,