Hi JT,
First... congrats. Well done on earning an appointment and on your desire to serve your country.
As for your questions.... Mostly covered above. Parents Weekend is the big-deal event designed for exactly what you describe.
That being said, some parents do go out for A-day as well. But if I remember correctly, for A-day you will only have a maximum of about 90 minutes to spend picnicking with your family (typically on/near the parade ground). While it's a nice day to see, it is can be a lot of travel/hassle/expense to spend a little more than an hour with the cadet in a limited setting. But if a family is close to CS, or the travel expense is not a burden, some do go. I would estimate perhaps only 1/3 of parents or less attend (other guesses, anyone?), so PLEASE let your parents know they shouldn't feel bad if they choose not to. Cadets with no family present will typically be "adopted" for that hour on A-day by other squaddie families, so all good.