Do mosquitoes have teeth

No.

A mosquito has no "teeth" as we describe them (for chewing food).

An adult male mosquito feeds on nectar or other sugars (fruit juice) using its long proboscis.

An adult female mosquito feeds on blood. To obtain this she has a needle like proboscis which contains a fascicle with 47 cutting edges (stylets) which allows it to pierce the skin of animals such as humans, to obtain the blood meal. This blood provides protein for the formation of the mosquito's eggs.