Velocity: Torricelli's theorem, v = √(2·g·h) m/s, where h is the depth of liquid above the opening in metres. Raise gravity and the jet's arc gets steeper and its droplets race along it faster; the tank also drains quicker.
Density: exit speed does not change with density — real physics, Torricelli's law has no ρ in it. What does change: the jet gets visibly thicker, the splash gets bigger, and the puddle grows faster, because pressure and mass flow rate both scale with density. Try switching between Oil and Mercury while the tap is open.
Range: R = 2·√(h·H) metres. 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 — 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.