A measurement is a special kind of quantum process involving a system and a measurement apparatus and that satisfies the von Neumann & Lüders projection postulate. This is one of the basic postulates of orthodox QM and says that immediately after measurement the system is in a quantum state (eigenstate) corresponding to the measured value (eigenvalue) of the observable.
Measurement does not change by considering the pair system+apparatus or by considering the triple system+apparatus+observer, because the fundamental interaction happenhappens between system and measurement apparatus, and the observer iscan be considered part of the environment that surrounds both. This is the reason why measuring apparatus give the same value when you are in the lab during the measurement that when you are in the cafeteria during the measurement.
See 2.
The system is always QM.
