1) Mary made me do something I don't like, Mary be damned.
This form might possibly be heard in certain English-speaking societies, but I have only ever heard it when the speaker was being deliberately old-fashioned or humorously melodramatic.
2) I'll be damned if he shows up at this party.
It's not clear whether you mean:
(a) you would be surprised if he shows up.
(b) you are determined that he doesn't show up.
If it's (a) then it's normally expressed as an exclamation.
"Well I'll be damned!… he wasn't even invited but he's just walked in the door".
If it's (b), where the phrase means a strong rejection of something, then a more likely expression would be: "I'll be damned if I'm going to invite him to the party". Another example: "He wants me to apologize but I'll be damned if I will, his behaviour was much worse than mine".
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