I confused the two, but it really doesn't matter. Rogues should not have expertise with non-rogue skills unless they commit to it via a feat like everyone else. The best rogue should never be better than the best wizard at arcana.
I disagree completely, this is one of the best features of the 5E Rogue.
Yes. Absolutely. Every class should get expertise in their traditional skills.
I want to break the idea of traditional skills all together. Tools (and I would include weapons and armor in this) should be from your class, but all skills should be available to all classes IMO with certain classes getting more than standard. I would like to see the classes modeled after the Bard where they could pick any skills instead of being limited to a subset to choose from.
I don't think other classes besides Rogues, Bards and Rangers should get expertise as a class ability, but I think it is fine in the subclasses and feats like it is now, which really lets anyone get it if they want it.