For now we have 3 german words for service: Dienst, Bedienung, Dienstleistung. Are there any differences?
Yes, there are. Bedienung is the service personnel you encouter in, for example, restaurants, bars, cafes. Dienstleistung is the service which is provided by, for example, your internet service provider, or the service a car rental service offers – Their Dienstleistung would be renting cars to someone. Dienstleistung is something that is (commercially) offered to you. Dienst is what you do, your obligations, your employement, your duty. "Dienst haben" or "im Dienst sein" means "to be on duty". This doesn't aply to all jobs and duties, but mainly to those, which offer a certain service to other people. Nurses, personnel of police or military and the like.