measurement problem - What is an observer in quantum mechanics?

My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts.

What is an observer? What are the conditions required to be qualified of observer, both mathematically and experimentally?

Answer

Observer is a special person (or a system that contains such person) which does not obey the usual laws of quantum mechanics. While it is much easier to define observer from a philosophical point of view, the mathematical answer is that the observer is a system which manifests subjective decoherence when observed. For the definition of subjective decoherence and precise mathematical formulations, refer to this work.