How mosquitoes find and get their food? For how much time they can survive without food?
Both Male and Female Mosquitoes feeds nectar and plan juice.
Only Female Mosquitoes feeds blood from Vertebrates. They find Lipid, protein from blood.
Lipid and Protein will help in nourishing egg nutrients. Their breeding proportionately increases with the amount of blood meal they intake.
I am not sure about their life expectancy without food.
Only female mosquitos (of some, but not all species) need blood to reproduce, they find it by following cues that lead them to warm blooded animals. These include gradients of heat and CO₂. Pretty much all mosquitos feed on nectar and plants while they are adults...
As for how long they could survive without food, I don't know, but no longer than their normal lifespans of a few days to a couple of months as adult.