It is contentious even to suppose that logic is concerned with being 'self-evident' at all. The old-fashioned idea that logic represents the immutable laws of thought that hold everywhere for all rational beings has fallen by the wayside. Logic has to do with accounting for how it is that some propositions follow from others, or how some combinations of propositions are inconsistent. Formal logic represents our best efforts to codify these relationships.
As our knowledge of logic grows, we may come to revise our grasp of these relationships, or codify them in a different way. Also, we have learned how to apply logic to different semantic properties or modalities. We may have a logic of provability, or a logic of obligation, or a logic of uncertain belief, and the rules for these will differ from those of simple truth and falsehood. As a result, there is no single logic that applies everywhere, let alone a self-evident one.
You say of the four sentences that you give that they cannot be proven, but they can be proven in the propositional calculus: all of those are theorems provided we understand the → to be material implication. If we read → instead to be some kind of generic conditional in a natural language such as English, then none of them are universally true.