Just a question:
Would it not be better to replace 2. with:
"I have a rookie card from him."
***neither a teacher nor a native-speaker***
The way you say means that the card was sent or handed by him.
The original sentence doesn't indicate that. Maybe the one who owns the card bought it, or traded a friend his/her less favourite card for this card, or etc.
(1) Oh, yes, native speakers often use "of mine, yours, his, hers, ours, theirs" to show "possession."
I want you to meet a friend of mine. (My friend) - One of my friends.
May I borrow a book of yours? (Your book) - One of your books.
Is Sue a girlfriend of his? (His girlfriend) - One of his girlfriends.
Is this a hat of hers? (Her hat) - One of her hats.
Everyone loves this country of ours. (Our country) Agree.
Have you ever ridden in that private jet of theirs? (Their private jet) Agree.
Have a nice day!
Bear in mind that if you use the indefinite article, as in examples 1-4 above, it does not suggest one single thing. May I borrow a book of yours? = May I borrow one of your books? BUT May I borrow that book of yours? = May I borrow your book (a specific one)?