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The defaults for switches (except for the pretty recent) is, if QoS isn't enabled, switch ignores any markings, it will forward them without change, and there's no different traffic treatment. With QoS enabled, switch will reset CoS/ToS (unless configured otherwise) and will provide some, default, different traffic treatment.
For your first question, whether you need to configure every switch, or even any, depends on your QoS goals.
For your second question, it's an "it depends" answer. Generally, for trunks, you trust whatever QoS marking are received, on ingress, and for egress, you prioritize and/or drop according to your QoS policy.
