Yes yes and more yes. I would also suggest that all cross-class abilities learned also show up in your equipable actions menu - even if you aren't currently that class. If I'm able to use them, I should be able to set them (edit for idiocy, b/c you can do this - but it's still not clear in the menu which are cross-class abilities and which are unique to class). This would also be necessary for your suggestion of saving action bars by class, I think - which I am in love with.