Density and buoyancy are sometimes considered an alternative for the presence of gravity.

The theory behind this is that objects that are denser than other objects will move down. So a solid object, which is denser than air, will fall to the ground. Less dense material (oil) will float on denser material (like water). Like in the video below.

This is true. You can see it all around you. And what the theory describes is perfectly in line with a gravitational model.
What the model however does not explain is how the objects have a direction. Why does an apple fall to the ground and not go sideways. And why would, in a vacuum, objects (like the classic ball/feather experiment) move at all? There must be a force action upon it, the objects actually accelerate towards a certain direction.

This force is pointed downwards in the medium we live in. But you can do other experiments to see the effect of density differences. Any laboratory know how to separate denser material from less denser material by using centrifugation. The effects are identical to what you might expect due to gravity, only the force (centrifugal) gives it an other direction.

Or how can we float in the air at zero G (like in a plane in a hyperbolic curve). Is the density of the air suddenly changed because we are falling?

The theory behind buoyancy is completely explained by the rules defined by the gravity theory. You can predict exactly what will happen in the different environment.

Below is a good video of the principles involved. Also there is a nice experiment where bubbles are enclosed in a bottle of water. Off course the air rises to the top of the bottle. However when the bottle is dropped, the bubbles do not rise any more, within there own environment. So does falling to the ground suddenly changes the density of water?