Translation:He asked a few questions about me.
Various nuances with word "propos"
- surveillez vos propos = watch your words
- à propos, comment va-t-il ? = talking about that, how is he doing?
- à propos de ta lettre, ... = "in relation to your letter" or "concerning your letter" or "about your letter" or "when it comes to your letter"
- mon propos n'est pas de vous contredire = my purpose is not to contradict you
In your examples, I can see the relationship between 'mon propos' or 'à propos' and their English equivalents. But mapping those to the sentence in question would still imply that "he asked a few questions about my words/intentions/comments/something-related-to-me". I still don't understand how "mon propos" leads directly to "me".
Are there other sentences that would illustrate the "mon propos"/"me" relationship?