What energy is usually associated with bond formation?

Bond enthalpy (which is also known as bond-dissociation enthalpy, average bond energy, or bond strength) describes the amount of energy stored in a bond between atoms in a molecule. Specifically, it's the energy that needs to be added for the homolytic or symmetrical cleavage of a bond in the gas phase.

In a somewhat limited form, yes.
Gases are a lot less dense than liquids or solids, aren't they? However a liquid could be less dense than a solid (usual case) or more dense than a solid (ice floating on water -- that is an exception)