OK, let's skip to (4), as that might help you formulate your skepticism more precisely. "Maximum entropy" has more than one meaning, but here it basically means a belief-state that assigns an equal probability to all possibilities. In other words, it's the probability distribution you would use if you had zero information. For example, if I ask you whether glappzug is thuxreq or not thuxreq, you can't do better than to just pick an answer randomly. You have no clue to go on, so just get the choice over with and move on.
A thorough-going skeptic, it seems to me, would have to think that all choices are just like that one. Even when we think we have information, we don't really (because we could be dreaming!). Therefore there's no reason to discriminate between any pair of alternatives, or among any set of them.
When you say "skepticism wins," do you mean that for any set of alternative claims, there is never any reason to discriminate among them?
Probability itself being somehow valid is something I do not think rationally legitimate. Therefore, in a sense yes but in a sense no.
I've raised arguments for philosophical scepticism before, which have mostly been argued against in a Popper-esque manner of arguing that even if we don't know anything with certainty, we can have legitimate knowledge on probabilities.
The problem with this, however, is how you answer a sceptic about the notion of probability having a correlation with reality. Probability depends upon axioms of probability- how are said axioms to be justified? It can't be by definition, or it has no correlation to reality.