John Brown was hanged in an open field, not in the town. And there were no buildings in Charles Town, VA (at that time - WV now) that looked even remotely similar to the building depicted in the opening scenes.
In the opening close-up of Ethan Hawke's eyes, he is clearly wearing contact lenses. The series is set in the mid-19th century, long before contact lenses were invented, much less in common use.