Are you able to purchase a Cabana on the same day you visit the park?

Yes

If they are available, yes. Try to do it in advance especially around busy summer holiday weekends.

Yes you can be early.

If you go in early yes

I'm not sure, that was my first time to Soak City, but im pretty sure that you can if your one of the first ones in line. It's never good to take chances, I would recommend to make a reservation, specially during summer time.