Rules Answer 1: Yes.
My Answer 1: Yes.
Rules Answer 2: He's invisible and looking at the 2014 condition, heavily obscured. The 2014 rules are very problematic when it comes to detecting people with other senses. People can't detect him at all with sight - that is, autofail Perception checks - but other senses still work normally. It's a mess! As he's not silent, and the air will move as he passes, he's not undetectable. Thus, no penalty on Perception checks (amazingly). And you were giving them for light obscurement. Have you noticed EARS?
My Answer 2: He's harder to spot than normal; people have disadvantage to spot him.
Rules Answer 3: Once you are hidden in 2014, you remain hidden until a new edition comes along. I mean, until someone uses a Perception check to find you, or you leave the conditions that allow you to hide. No additional checks UNLESS someone finds him, when he has to hide again. Note, you can be hidden from one enemy while spotted by another.
My Answer: He stays hidden until found (either by an active or passive check).
Rules Answer 4: In tactical combat, there's no reduction in speed (possibly). In exploration movement, he's slower - at the "Slow" rate - 200 feet per minute.
My Answer 4: He's not moving fast whatever he does.
