Could atoms in a original pure molecule of diamond be entangled?...these atoms are close to each other and interact all the time, could it be there is a greater chance of finding that most of these atoms are entangled?
It depends on what degrees of freedom are isolated enough to avoid decoherence.
Individual carbon atoms are bonded to each other in a lattice in the diamond, and subjected to ongoing thermal vibrations, so their individual motion states and the state of their valence electrons are not going to be particularly isolated. Also, carbon 12 nuclei has zero spin, so presumably you can't store qubits or entangle their spins. However, carbon 13 nuclei do have spins, as does nitrogen vacancy centres, and they can be entangled and used. Even better, phonons in diamonds, being collective motion modes, can be quantum entangled.