How do toenails grow? could you provide an illustration or video perhaps?

No video: But nails grow from the area under the skin behind the nail called the nail matrix. Damage to this area will cause funny shaped nails, nails to fall off, ingrown nails etc. Hope this helps.

Nail growth: Toenails grow because a protein called 'keratin' continues to be laid down at the nail growth areas (matrix) at the base of the nails. They grow the same way that fingernails grow, just at a slower rate.