Are there any fees for admittance, parking etc. to get into this park and are there designated hours open to public or just dawn to dusk rules?

Designated hours. Not public beach..restricted.

Mostly only open to public on Sundays in summer and part of fall/spring. Free but get there between 11-12 because if reaches capacity they will turn people away. 11am -5pm are the hours. They close extremely early.

No fees. Only stipulation is that you take all your trash with you. They have designated hours.