The average amount of overjet is 2-3mm from your photos my assumption is that currently your overjet is between 3-4mm. This can typically be reduced using Invisalign or other clear aligner methods. I would first attempt correcting the space with orthodontics before choosing surgery. Jaw or joint...
Dark triangles are caused when crooked teeth are straightened, or when the triangular space between teeth is to wide relative to the length of the triangle. Poor oral hygiene can contribute.
The solution is to reshape the teeth then pull them closer together.
Eliminating these triangles is...