All are grammatical and make good sense. The second, however, violates the laws of physics. Liquids drip vertically. That's how gravity works. Things do not drip horizontally, which is what would be happening if water dripped "across" a hole.

"Water was dripping through a hole" is correct. "Water was dripping from a hole" is correct, but it implies a point of view. It suggests that the hole is above you--in a roof, perhaps--and that you are watching the drip from below. "Water was dripping across a hole" is wrong. In English, we do not use "across" for motion that is inside something. We see "through" a window, not "across" a window. We run water "though" a hose, not "across" a hose. If there is a hole in a road, but it is not deep, you might "drive across it," but that is horizontal motion. Water cannot move that way. It can't flow or drip "across" a hole.