Kinda. All coastlines are public-access, but if you own the property up to the coast (say, a cabin on a river), you do not have to grant access across your property. So, you could walk down the river and hang out in front of this cabin, but you can't trespass across private property.
Correct, but if there's a pre-existing easement (right of way) you can't buy the property and then close it off. I mention it in this context because of the agreement the inn had signed to make its parking area available to campers and hikers, which it appears to have reneged on.
Really? What a great law!