No. Typically, male and female mosquitoes feed on nectar and plant juices, but the females are blood-suckers while the males are not. The females need blood to obtain nutrients from blood before she can produce eggs. Both plant materials and blood are useful sources of energy, but blood obtains proteins as materials for egg production.
No. Male mosquitoes live on plant juices, sugary saps, and liquids arising from decomposition of plant material. They do not have a biting mouth that can penetrate human skin. But the females do. In some species, the females need a meal of blood before they can lay their eggs. Blood lipids (fats) are converted into the needed iron and protein to produce upwards of 200 eggs.
Sources: Feldman, David. Do Penguins Have Knees? p. 190; Passarin d'Entreves, P. The Secret Life of In-sects, p. 28.