The only question which used the word "Humean" concerned the laws of nature, so none of Hume's other views are relevant, though I admit to not being sure why RobbBB is so certain that the Humean view of laws of nature is wrong. The Humean view is sometimes called the regularity view; the short version is that it is the view that what it is for a law of nature to be true just is for there to be a pattern of events in the universe conforming to the law. The non-Humean view insists that there is something more, some additional metaphysical component, which must be present in order for it to be true that a regular pattern reveals a genuine law of nature.

One simple argument for the non-Humean view is that it seesm that some patterns are coincidences, and we need some way to distinguish the concidences from the genuine laws of nature. The standard Humean response to this is to say that there are ways for a Humean to identify something as a coincidence. A Humean identifies a coincidence by noting that the pattern fails to cohere with broader theory; laws of nature fit fairly neatly together into larger wholes up to the general theory of everything, while coincidences are patterns which in light of broader theory look more like chance. Further, the Humean will argue that when there aren't clues like broader theoretical concerns, saying that it's a law of nature if it's got the right metaphysical extra and not otherwise is useless, since there's no way to detect the metaphysical extra directly.

Hope that helps.