For the most part, yes, almost all of the activities you listed above would be part of the physician's orders in an American hospital. A few things, like routine hygiene measures, turning the patient, basic comfort measures, etc. could be done without orders. However, within those order sets, the nurse has some leeway as to how things are done. The nurse is also expected to use judgement to continually monitor the patients and to make adjustments as appropriate, notifying the physician and discussing it as a team if the nurse feels a actual change in the order is needed.
Much of the motivation for that system is not for increased safety (though having both the physician and the nurse working together to formulate the plan of care might increase the safety.) Much of the reasoning is purely political, the physicians want control of what happens to the patient. The system is also designed with the finances in mind. The physician's order is what authorizes the nurse/hospital to provide the service and get paid by the "3rd party payer" (insurance company, government program, etc.). Whoever is paying the bill doesn't want hospitals to provide extra services that add to the cost. Physicians (or sometimes, Physician Assistants or Nurse Practitioners) have become the "gate-keepers," deciding which treatments are going to be performed and paid for. The payers police the physicians and hospitals to keep the costs down.