Monks, their hospitalization and their medical treatment

I have questions regarding hospitalization and its morals 1. Are monks/nuns allowed to be hospitalized and can they go to a hospital or doctor if sick? (because aren't they not allowed to request anything according to the vinaya?) 2. Can a monk/nun take painkillers or will that be a breach of the fifth precept? 3. If there is a parasite or other being inside of someone, can they take medicine to cure themselves of it, or would that break the first precept, or is it not if the being isn't sentient?