Are they even human? Is the mouth naturally like this or has it been surgically altered to indicate the person's social position as a tribe leader?

These body modifications are actual things in African (and other) culture called Lip Plates.

The lip plate, also known as a lip plug or lip disc, is a form of body modification. Increasingly large discs (usually circular, and made from clay or wood) are inserted into a pierced hole in either the upper or lower lip, or both, thereby stretching it.

^Wikipedia

I don't understand how this mouth allows for eating or any other activity usually associated with the mouth.

They are removable

We don't know Wakanadan customs obviously but, in general real life, they're generally only worn for tourists & special occasions such as ceremonies.

Naturally, the stretched lip would make eating (and drinking) somewhat messy (one would imagine) but it doesn't make chewing impossible.

Nor, depending on the food do they have to be removed