ALL animals must eat to remain alive. If a bat (or any other animal) does not eat, it will die of starvation.
A vampire bat can typically survive for about a week without feeding on blood. After this time, they become weak and may die if they do not find a blood meal.
When a bat is going through it's hibernation phase, bats have the ability to sleep through the entire winter without needing to consume food and water. Should a bat find itself without food or water in normal, every day conditions bats usually not be able to last any longer than a couple days. Most bats will need to consume food or water within 3 days for survival.
food
with no food, probably only a few days. some thing like mice. probably one week.
Kind of like a cave. Probably forever.
too long
The time it takes for a bat to starve to death can vary based on species, age, health, and environmental conditions, but generally, bats can survive without food for several days to a couple of weeks. Most bats require a steady intake of food, such as insects or fruit, to maintain their energy levels and metabolic functions. If unable to find food, their condition will deteriorate rapidly, especially in warmer temperatures where their metabolism is higher.
3 days
no idea
Nothing it won't live long enough cause it doesn't have food or shelter to live.
no
Cockroaches can be terrible pests, and even worse if there is an infestation. A cockroach would not survive being hit with a baseball bat.