Did you hear anything about his getting married?
Is the above question the same as saying
Did you know that he is going to get married?
or
Did you know that he has got married?
or something else?
Did you hear anything about his getting married?
Is the above question the same as saying
Did you know that he is going to get married?
or
Did you know that he has got married?
or something else?
Neither of your paraphrases is necessarily accurate, though either may be.
Did you hear anything about his getting married?
This asks literally if your hearer has heard anything about a marriage. It would ordinarily be used if you had heard something unreliable—a rumor or a suggestion that might be mistaken or that you might have misunderstood. And it might concern a marriage that 'he' has already undergone, or one that 'he' has planned or scheduled, or one that 'he' is merely thinking about. You ask your hearer if he's heard anything which might make you more certain.
Your paraphrases however presuppose the fact of a past or future marriage and ask whether your hearer is aware of the fact.
Your first question is ambiguous. Without additional context, it could mean either of the two alternatives.
If you are the person being asked, you will need to seek clarification, perhaps by replying, "No I didn't hear. Has it already happened?"
If you are the one doing the asking and want to remove the ambiguity, you should rephrase your question. You can use the appropriate one of your alternatives, or add a few words at the end that clarify the timing of the third person's marriage. For example, "Did you hear about his getting married next month?"