You can try keeping the clock open when you turn the car off. I'm not sure about clock, but if you do that with the radio, then the radio comes on the screen next time you turn the car on. If that doesn't work, seems like your only option is to open the clock app every time you turn on the car.
I don't think so. I'm going to assume you have either the Dispay Audio or Nav system. I have a 2020 Passport touring which comes with the Nav. I haven't found a way to have the clock/wallpaper as the default screen, but you can move the various programs around so the clock/wallpaper selection is on the home screen when it pops up. One touch of the button and you are there.