Of course, mosquitoes feel pain just like every other creature in the animal kingdom, as the sensation of pain is one of the most basic and integral to the survival of any species.
Mosquitoes can feel pain in any number of different ways, from being burned, compressed, starved, etc.
Pain provides stimulation that allows for a mosquitoes avoidance of situations that cause damage to the body and reduce the likelihood of survival.
Don’t make the mistake of thinking that just because a creature is very small, even a small’s a mosquito, that it cannot feel pain–because it does.
