We actually booked at the station on the day. They were able to get me on the next train and booked me into the private compartment. If you have family with you, they will need to pay for regular reserved seats, but will be allowed to sit in the compartment with you.

When we were being squired around Chiba in our friend’s car, my blue badge from the US was accepted and we would be pointed to the designated spots, if they weren’t immediately obvious.

Yes to both.

I was able to park my scooter right outside the shops, alongside peoples bicycles. Never had an issues.

I’m from California and used my blue parking badge permit as “proof” for the handful of discounts I got. I will admit I had no idea I could do that until midway through the trip, when an employee at the Toji Temple gate suggested it and asked if I had some sort of verification. I expect that should be fine to use for other places.