The movement of the particles in a 2D liquid is similar to 3D, but with limited degrees of freedom.
Vibrational motion is in most cases not constrained in comparison to 3D.
If the density of a 2D liquid is decreased, a 2D gas is formed.
This was observed by scanning tunnelling microscopy under ultra-high vacuum (UHV) conditions for molecular adsorbates.
If the density of a 2D liquid is increased, the rotational degree of freedom is frozen and a 2D solid is created.