Yes, there is parking right by the chapel.
Yes, there are restrooms at the groom's quarters to the right of the chapel for guests to use. It's a bit of a walk down a hill.
Yes, our wedding guests have free access to explore the gardens the day of our wedding. (I would recommend tennis shoes)
The best way for out of state guests to get to the venue would be to fly into the Clinton Airport in Little Rock and then to rent a car. It is about an hour drive to Hot Springs.