Pony rides during the week?

Yes, but you need to pay extra.

Pony rides are $6. Admission rates: Children (2 and Under): FREE Children (3-12): $16.95 + TAX Adults (13-61): $18.95 + TAX Senior Citizens (62+): $16.95 + TAX Military Personnel: $16.95 + TAX Full rate information is available at this link: http://www.longislandgamefarm.com/zoo-plan-visit-long-island-animal-shows-event-calendar/#rates

How much is paid to enter the park.

Yes

Yes there are, it's a separate fee.