my face vs. my own face...is "own" redundant?

Own provides emphasis and, especially in the cases involving relatives, a sense that there is something unexpected going on.

"Remember now, it was my own mother who said... ."

"Turned into the police by his own son... ."

"To have my own daughter go behind my back... ."

"I find out that the Employee of the Year turns out to be my own son."

"Ah, look who's here, my own Da!" cried Caroline.

====
You can leave it out it every instance, but the sentence seems flat and the meaning loses punch.

Joe(my own self)Nation

You are correct in your supposition that the word "own", in the examples you gave, is used to give emphasis to the particular ownership of the bag or fatherhood of the son who kicked the ball, when it is desired to draw attention to the definite assertion of ownership or belonging.

The little boy ran across the room to retrieve his bag. (The bag might be the only bag which is there)

The little boy ran across the room to retrieve his own bag. (Only his bag) and/or (not anybody elses bag) (Maybe there are lots of bags)

All of the boys ran across the room, each to retrieve his own bag.

My son kicked the ball.

My own son kicked the ball. Not anybody elses son, my son! My very own son! The champion! Hurrah! I'm so proud! My son is a footballer! (etc)

It is a wise man that knows his own father...

NB the word "retrieve" is spelled thus. A simple rule is "i before e except after c"

Thus:-

relief
retrieve
believe

receipt
conceit
deceit