Does the park have beach access?

Yes it does

Yes, it's a decent walk, no great handicap access

Yes, there is beach access. You need to cross a river on foot at the start of about a 1-1.5 mile flat walk. Most people remove their shoes to walk across the 30' wide river. Having water shoes makes it easier.

There is a beach access. But first you have to cross a river, on foot.

Yes but its about a 2 mile hike

Yes, i believe so