Sorry, but I'm pretty sure these are both post-mint damage.
The first coin looks like it's simply been mangled, caught up in machinery or something.
The second resembles a clipped planchet, though the radius of the circle looks to me to be much too small. round clips, if genuine, are going to be the same radius as the coin itself, since the same punch that punched out the coin punched out the clip. So I'd say this one was caused by somebody having some fun with a drill.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis
half penny: was probably a victim of a metal press or an anvil. PMD
5 cents: we will probably need clear closeup of the missing section to determine if it is PMD or part of the original planchet or coin blank was missing prior to the minting process
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