There is one fundamental and many non-fundamental kinds of existence. Things (material bodies) exist fundamentally. Many other objects exist non-fundamentally: properties, events, relations, states; abstracts (universals), laws of Nature; possible states, virtual particles; minds, mental processes; ideal objects created by minds (Popperian "World 3"). All of them are always based on material bodies, but they exist really.
The author analyses three concepts of situation in the philosophy of science: the problem situation (due to Karl Popper), the discovery-generating situation (due to Elżbieta Pietruska-Madej) and the solution-yielding situation (due to Jan Such). His thesis is, that the set of solution-yielding situations is a subset of the set of discovery-generating situations, which is contained in the set of problem situations.
There are two concepts of the scope of a law: 1) the set of bodies (in our world) in which the law is fulfilled, 2) the set of models of the law, or the set of possible worlds in which it is fulfilled. Their use leads to opposite answers to the question which law is broader than the other.