Is there a place on Earth, where polar axis lies on the horizont and heaven equator is in zenit? If it exists, can I, in theory, see all the constelations available worldwide this night?
With the axis of rotation of the earth matching the axis of rotation of the stars, and the equator of the earth matching the equator of the stars, any place along the equator would match what you have described. However due to closeness to the horizon, the polar-most stars wouldn't be visible. If you were able to get a hundred metres or so above the ground, with nothing in the surrounding landscape, you could see all of the stars in the sky over a year's time.