Is there a discounted rate after 2pm? (Not with an annual pass just for the day)

No

No discounts at Disney.....they don't need to, parking is not even discounted in evenings.

There doesn't seem to be an afternoon discount, but the one day Water park pass is good for admission to both Typhoon Lagoon and Blizzard Beach throughout that day

Have not seen any discounted rates for late entry.

I havent seen a discounted rate for late entry.