Will the game force me to change cars at some point? I have played the first 4 championships in a modern supercar and haven't bothered changing my car. Is there any benfit to buying another car and changing the championship?
You can focus on supercars if you want, or you can change it up at the start of each championship.
Eventually you will run out of supercar events, and at that point, the game would force you to change.
If I mess up in a race (and don't restart) can I do the race again from the map screen?
No. Not without re-starting the championship.
Do I get anything if I start to turn off all the assists, and is there a penalty for using rewind? The game feels really easy now but I don't want to make it frustrating.
You get a CR bonus. You can see the bonus multiplier in the difficulty settings.
The penalty for using rewind in FH2 is minimal: having it on lowers the CR bonus and using it wipes out a skill chain.
Maybe you could raise the difficulty a tick. Race a championship. See how it feels. Rinse and repeat. Keep in mind that some Forza assists (in many players' opinions) are more a hindrance than an assist anyway.
This is more of an XB1 UI question but is there a way to turn off gameplay clip notifications, but leave achievement notifications on? The options seem to be all off or all on.
Disable Game DVR in Settings -> Preferences.
That shuts off app and user Game DVR, which is why we really need two do different settings or per-app settings.