What phone do you have? Not all features are supported on all phones--for example, my iPhone 6 on AT&T (if carrier matters) doesn't support any of those email feature on the Mazda Connect system. (unamused)
You can check your own phone model here if you aren't already aware of this website (after plugging in your car info, go to the Communications section and then the red "Is My Device Compatible?" button):
http://infotainment.mazdahandsfree.com/