You are describing the stabilizer(sway) bar bushings. It's simple to service yourself or you can have a mechanic do it in 15 minutes tops. A Mazda dealer that replaces struts for that is staffed by idiots. Regarding the other rattles, the stock size tires and especially the stock brand are prone to causing so many rattles because they are hard. Put 215s on and you won't have all of the rattles during driving. Hell, any car will rattle with tiny hard tires on it.
Thanks, I'll bring it in and ask them to check out the sway bar bushings. Currently running 205/55R16 Dunlops for better ride comfort. The squeaks seem like they're plastic related, I'll get them to check the interior paneling to see if a clip has fallen out or something.