Monstrous isn't an ability that a creature has. It's just something true about that creature. If the creature stops being a creature or loses its abilities, it will continue to be monstrous.

An ability that triggers when a creature becomes monstrous won't trigger if that creature isn't on the battlefield when its monstrosity ability resolves.

“Protection from enchantments” means that Polis Crusher can't be enchanted, it can't be targeted by Aura spells or by abilities of enchantments, all damage that would be dealt to it by enchantments is prevented, and it can't be blocked by enchantment creatures. Notably, it doesn't have protection from enchanted creatures (unless those creatures are also enchantments).

Once a creature becomes monstrous, it can't become monstrous again. If the creature is already monstrous when the monstrosity ability resolves, nothing happens.

Polis Crusher must be monstrous as it deals combat damage to a player in order for its last ability to trigger. Once the ability triggers, it resolves even if Polis Crusher isn't on the battlefield at that time.