How mosquitoes get their food and survive?
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.