Is there a fee to get into the park

Yes, it's a few dollars per person.

Yes, "Admission to the park is free for ages 3 and under; $5.50 ages 4-12; $7.50 for adults, and $5.50 for seniors. Groups of 15 or more are $3.50 per person. Guided Tour or School Program add $1.50 per person. Summer Photographer's Pass $50.00 per hour per person (by reservation only). Winter Photographer's Pass $150.00 per hour, additional people $50.00 per hour (by reservation only). Small Shelter Rental $25.00 per day. Large Shelter Rental $50.00 per day. Stroller, Wagon, or Wheelchair Rental $3.00 per day ($5.00 security deposit required). Free admission for military personnel with a valid ID. Accompanying family members receive a discount with an admission rate of $5.50 per person."

Yes, there is a park entrance fee as noted above. Prices range from $5.50 to $7.50 per person.