You can add points as tourist/ historical/art. You just can't add them as a poke stop. OSM cannot violate copyrights, and we do not have permission to access Niantics database and add their data. At least that's my two since.

Are you sure smoking should be set to isolated?

Is there a public beach on day island?

I recently passed through this area I did not see a trail, but I was not looking for one. Bing streetside seems to show what may be a trail, but it is dated (unfortunately my camera's battery died just at that spot that would have given a view of it). I'm just wondering because of this sign on the bridge, "All residential beaches are private." https://www.mapillary.com/map/im/G6m4zQOJpwkvGvk2zsXSyQ

-Jacob