Air plants take all their water and nutrients through the leaf system, none or very minimal amounts are absorbed by the root system. This root system is used as wire like anchors to hold onto trees, rocks etc. Since the root system is not important to the plant this can be removed without harm, to make make your plant easier to mount. The roots may or may not grow back, either way is doesn’t matter to the welfare of your plant.
Air plants DO have to be watered, they live ‘in’ air, not ‘on’ air.
Air plants are NOT toxic to animals, although this does not mean your pet won’t eat them, but they will survive the experience, your plant might not.
Air plants are NOT parasitic, they do not harm the host tree.
Trim away brown, bent or damaged leaves, this will not hurt the plant.