No. You must register at the designated state park campground. It is recommended you reserve ahead of time: https://reserveohio.com/OhioCampWeb/Facilities/SearchViewUnitAvailabity.aspx
Certain state parks have back country camping but it is still designated areas.
No. This is why there is designated parks. However if the camping spot is in an remote area that is unclaimed or privately owned with permission it is legal.
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