You pretty much described how AA works.
1) Driving mode, yes.
2) Driving mode will mute your notifications, yes. It will still allow calls & texts, yes.
3) 1: When you get a text, it will play your text alert tone through the car audio system and show a pop up at the top of the vehicle's infotainment system.
3) 2: You can tap the pop up, or say "hey Google read my messages". It will then tell you who the text is from, and ask to read the message to you.
3) 3: You will then be asked if you want to reply.
3) 4: See above.
Replying to messages is pretty accurate via voice. Optionally, you can call that contact via voice command as well; all without touching the phone. To answer, you do have to tap either the icon on the screen or your steering wheel button.
Hope this info helps.