For the first part please see: Can Scientists Pursue Science Successfully Apart From a Robust Epistemology? Part 1
The reason why inferential beliefs are so important is that one’s scientific method cannot be contrary to one’s epistemic method. With that said, certain models for scientific explanation must have justificatory acceptance. For example, a deductive form of scientific inquiry cannot be the only means acceptable since one cannot have a deductive form of epistemology since all beliefs would be self-justified and self-preserved (at least this would not account for a robust epistemology).
Such methods are derived from the use of abductive reasoning. The American philosopher and logician Charles Sanders Peirce first described abduction. He noted that, unlike inductive reasoning, in which a universal law or principle is established from repeated observations of the same phenomena, and unlike deductive reasoning, in which a particular fact is deduced by applying a general law to another particular fact or case, abductive reasoning infers unseen facts, events, or causes in the past from clues or facts in the present.
Certain unknown entities may become known by inferential means. We can infer the existence of protons, quarks, and other elementary particles by predicting what effects such entities may have in certain situations. This may be causal in nature and may be confirmed by inference. However, it is not the case that we directly experience the existence of these particles (for all intents and purposes, it certainly is the case that we experience particles when we run in to a wall and even then we experience the strong nuclear force over the particles). There is no direct evidence for the existence of these theoretical entities. Additionally, theory cannot discharge its explanatory function without them (though this serves no problem for anti-realism).
Nevertheless, epistemological direct realism and new belief formation can be non-inferentially justified. The reason why non-inferentially justified beliefs must also be accepted is that such beliefs may be basic from which we may make further inferences. Other propositional beliefs may be basic but non-empirical such as mathematical truths. What is interesting about having mathematical truths being non-inferentially justified and basic is that mathematics seems to be the language in which physical phenomena and laws are expressed. If it’s true that physics and the empirical world are expressions of mathematics, Platonism aside, then it seems that the most fundamental aspect of the empirical world is not empirical itself.
When using certain theoretical terms, as in the inference to quarks, the epistemic process cannot restrict explanations to only natural or empirical explanations. If one attempts to strip science of all metaphysical import then material causation is the only sufficient form of scientific explanation. However, this has an unnecessary restriction on science and is incongruent with one’s epistemology (if it is to be robust). The robust epistemology certainly accounts for inferential explanations that are not necessarily required to be material. The epistemic methodology may be identical to a non-scientific context but when this methodology is applied in a scientific context then the explanation is ruled out a priori with no [apparent] justification (hence the removal of efficient and final causation from science). Thus, scientific explanations must not necessarily be material explanations. Remember, by using inferential explanations such as quarks and protons we observer their effects and infer as to what the best antecedent causal explanation may be. It’s an issue over the identity of what antecedent causes could be. (In a normal epistemic process the antecedent may be agency). Being an epistemological and scientific realist does not exclude one from being a metaphysical realist.
 Charles Sanders Pierce, “Abduction and Induction” in The Philosophy of Pierce, ed. J. Buchler (London: Routledge, 1956), 375.
 Alex Rosenberg, Philosophy of Science (New York: Routledge, 2012), 158.