This is a very interesting question. Basically what you are saying is if we have some material that can repel air, can we make it float?

My short answer is "possibly but not easy". To make things float, you have to supply large enough net external force that can fight the gravity.

To largely reduce the gravity is not easy, unless we move to another planet. So the other possibility is to supply large net external force that can fight the gravity. The first thing I want to mention is the rocket. By combustion of the fuel, the air is strongly propelled at the bottom of the rocket, thus providing a strong enough thrust against the gravity that can send the rocket into space. If we have the material that can repel air and apply them to the bottom, we can provide a net force that is against the gravity. But because the density of air is relatively small, usually it is not strong enough to go against the gravity and float in the air.

No, it would not work. What would happen would be like if you poured water onto oil (water and oil repel each-other). Water is denser than oil, so it will sink to the bottom and form a layer on the bottom, while the oil sits on top. So unless your oxygen-nitrogen-repelling substance were also lighter than air, then it would fall to the surface of the Earth just like anything else. Gasses that are lighter than oxygen and nitrogen like hydrogen, helium, and even water vapor do get used to make balloons.