If you want fully automatic "set it and forget it" shooting but want to be able to influence it, use P mode. It's automatic but you can tell the camera "make it darker than normal" if you see it overexposing.
Focusing is completely disconnected from exposure itself but not from modes: Auto mode is probably doing whatever the heck it wants and that is really not what you want, so use a PASM mode where you can adjust the autofocus system to do what you want better.
I don't know what to advise you there because focus varies between companies. Know that AF points are places where the camera can check focus. You need to put the selected one over the subject, focus, and then shoot.