Why a molecule has $3N$ degrees of freedom? An atom has $3$ degrees of freedom because it can possess energy in $3$ independent ways- Kinetic Energy in three independent directions. Therefore, a collection of $N$ atoms will have $3N$ degrees of freedom. But this is innately when the motions of atoms are entirely independent of each other. How can we extend it for a molecule of $N$ atoms where the energies belong to the molecule as a whole, and the atoms are not independent of each other?
I found a similar question, but that is poorly framed and answered.
 A: Any molecule has just the same number of degrees of freedom, $3N$, as a gas of $N$ isolated atoms, even despite their interactions.
The simplest way to see this is to imagine displacing the atoms only very slightly, so the molecule flexes only just a bit. Do you think you can, say, displace any given atom by a tiny amount - say 0.001 nm - from its usual position, in an arbitrary spatial direction, and do so for every atom, too, given that the bonds are flexible?
Hence, each atom still contributes 3 degrees of freedom. The interactions will change how those degrees of freedom manifest across the bulk molecule for motions that are not small, but this provides the quickest way, I think, to derive the underlying result.
A: 
An atom has 3 degrees of freedom because it can possess energy in 3 independent ways- Kinetic Energy in three independent directions.

No. Kinetic energy is a scalar and has only one value. An isolated atom has 6 degrees of freedom, that means it takes 3 coordinates to specify its position and 3 more to specify its velocity. But we don’t really care about the position of the atom as only it’s velocity results in dynamics. Thus 3 degrees of freedom.
For two atoms, this would mean we need 6 coordinates to specify the state. Even if the two atoms form a molecule, the individual atoms can have any motion. 
A: 
In physics and chemistry, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all states of a system is known as the system's phase space, and the degrees of freedom of the system are the dimensions of the phase space.

It is as a coordinate needed to describe the behavior of the particle, in this case the velocity. The difference between N atoms in a gas and N atoms in a molecule lies in the boundary conditions, the gas has the container,in  the molecule the binding imposes the boundary. To describe the wavefunction of  the atoms in the molecules still a coordinate system is needed, and even though bound, the same number of degrees of freedom are needed mathematically.
