No. Only suspenders ("braces" in the U.K.) are acceptable with a tuxedo. They should be the button-on variety, as clip-on suspenders will damage the pants. Black or white silk are the most classic....
Usually, cardigans zip or button, but if they don't, its a good idea to. You aren't forced to , of course and many people don't .You usually wear them on your natural waist. It can be thick or thin....