yes unless you have the Empire State Pass
For events there is usually a car charge(ex.$10 per car), but there are special events that require a fee. Certain times of the year there are no fees. To go through Coe Hall there is a $3/pp charge but the house is only open until late September and then it is closed for the winter. No pets on property at all.
Yes. There's a 8 dollars per car fee unless you have an Empire Passport ...then it's free.
See Darrel B"s answer above
Get quick answers from Planting Fields Arboretum State Historic Park staff and past visitors.