How does vibrations for singing work? does that really come from the belly? or are you just born with the ability to vibrate?

It may take work: Assuming you are talking about a vibrato. . . The bulk of the vibrato likely comes from the vocal cords. However the abdominal muscles also play a role. There has to be a fine balance between abdominal muscle tension and the tension of the muscles surrounding the vocal cords. Some may master this after years of practice and others are just naturals.

Vocal cords: This come from the throat and the vocal cords, and related to the elasticity of the vocal cords, the strength of the cords. Singing from the diaphragm adds power and resonance from the nasal and upper airway passages.