how do the molecules at the surface exist because there are only molecules below it and not above it? Won't they accelerate downwards?
You could ask the same question for the surface of the earth.Why is it not imploding? The answer is "quantum mechanics". When one is talking of molecules and atoms one has to talk in terms of quantum mechanics.
Atoms exist because the electrons orbit around them in very specific quantized orbits which might be distorted when new forces enter but need a lot of energy to be destroyed, which gravity does not supply, as a very weak force.
All interactions in liquids and solids and gases between atoms and molecules are electromagnetic even though the atoms and molecules are neutral, because there are spill over electromagnetic fields from the shape of the electron orbits of the atoms/molecules. The spill over fields may be attractive and create the coherence of molecules and explain the creation of solids. In liquids these spill over attractive forces create surface tension, and the horizontal (actually surface of sphere with radius to the earth center) level of the liquid.
When external forces become large, the electron orbits come to play with their negative electric fields which repulse each other; also the Pauli exclusion principle assures that only one electron can be in an orbit, so compressing find resisting forces .
For a liquid surface the compression comes from the force of gravity, as @QEntanglement explains, the weight of the column of air over the liquid.