Does it damage the gerbil if eats leaves from trees?

No, it is not harmful for gerbils to eat leaves from trees. In fact, many types of tree leaves are a natural part of a gerbil's diet. Some gerbils even build their nests out of tree leaves. However, it is important to make sure that the leaves you are feeding your gerbil are safe for them to eat. Some types of tree leaves, such as those from oak trees, can be toxic to gerbils. If you are unsure whether a particular type of tree leaf is safe for your gerbil, it is best to err on the side of caution and avoid feeding it to them.