Velocity: Torricelli's theorem, v = √(2·g·h), where h is the depth of liquid above the opening — not the full tank height. Raise gravity and you'll see the jet's arc get steeper and the droplets race along it faster; the tank also visibly drains quicker.
Density: exit speed does not change with density (that's real physics — Torricelli's law has no ρ in it). What does change: the jet gets visibly thicker, the splash where it lands gets bigger, and the puddle grows faster — because pressure and mass flow rate both scale with density even though speed doesn't. Try switching between Oil and Mercury while the tap is open.
Range: R = 2·√(h·H). Interesting quirk: g cancels out of this formula algebraically, so the landing point barely shifts when you change gravity, even though the arc's height and speed clearly do. That's a genuine, well-known result — not a bug.
Draining stops once the water surface reaches the opening — liquid below the hole has no way out.