i don't know any of the terms in the first paragraph (except "adjective"), so i can't help you there.
fortunately, you've provided examples. (:
your 2 examples are fine, but the word "explain" is unnecessarily specific.
i.e., the "__ing" doesn't always have to be the reason for the subsequent action (though it can be, as in your example #1).
it can also describe another, ongoing action that serves as background for the main action.
e.g.,
Walking down the street with my dog, I ran into an old friend I hadn't seen in years.
--> "walking" doesn't literally explain this encounter--it's just what was going on at the time--but this sentence is still fine.