Can you buy America is beautiful annual pass at the park ?

Yes, you can. They accept credit cards or cash.

Yes, check the website though because they also take reservations and if you show up and they are out of reservations you might not get to go.

Yes

I go

Yes. You can purchase a pass at any of the parks. I just purchased mine here on April 7, 2022. It is valid for one year. The process was fast and easy.

Yes, it's part of that program.