Difference Between ‘As’ and ‘Because’ – Word Choice and Conjunctions

While those might mean the same for the laymen, from a medical point of view, there is a difference between illness and sickness.

Medical sociology has long made the distinction between illness and sickness. Illness is the objective diagnosis that an external impartial observer is able to make based on the constellation of symptoms which the patient presents. Sickness is the social role that the patient adopts as the patient and other concerned stakeholders, in relationship with the patient, interpret the meaning of the illness.

From what I get of it, someone might see themselves as sick (with the social/role aspect of it) but not actually be ill (in a medical sense). Also, this paper might provide some useful reading.

They are not interchangeable. "Due to" has to be followed by a noun phrase and "because" - by a clause (which means there will be a verb after it). So in your examples, the second sentence is correct. A correct example with "due to" will be: "His company's success was mostly due to the excellent performance of the manager."