You raise some interesting points and seem to suffer from some confusion about this topic. Concerning pneumatic and hydrostatic testing, it's "either/or". You either hydrostatically test the vessel OR (if absolutely necessary) you pneumatically test the vessel. A discussion on these two types of testing was recently active in this forum, and I suggest you review what is said there.
You correctly note that the test pressure, whether hydrostatic or pneumatic, is greater than the MAWP. If you think about it a bit, you'll note that the vessel is not designed so that it will explode just above the MAWP (duh). In fact, you want to test it at a somewhat elevated pressure using an innocuous fluid - e.g. water - so that if its integrity is found lacking you have not released some toxic or flammable fluid. You don't want to do that "test" with a hot nasty operating fluid filling the vessel, so you test with water or air. Codes may vary some, but I'm accustomed to the hydrostatic test pressure being 1.3 x the MAWP. (It was formerly 1.5 x the MAWP.) There are correction factors for the lower temperature conditions during testing when the design temperature is elevated. I'm not sure how corrosion allowances are handled. Test pressures are different (lower) if you test pneumatically. In any case, the vessel is actually designed to be able to fully withstand the test pressure, providing a bit of a "buffer". Never try to infringe into this buffer; it is both dangerous and illegal.