Hmm, in actuality:
Young Brother's Quirk was to "transfer" his quirk to others, All For One's Quirk was to give/receive quirks. And in the process of forcing a quirk to his brother (AFO picked "stockpile" power) just to make him fall to his death, AFO didn't even realized his younger brother had a quirk that can transfer his own to others (it was explained in the Hero Killer arc).
Stockpiling and Transfer are the two main quirks which started One For All, so it all makes sense that the Vestiges' quirks were also stockpiled and passed on to generations (up to currently, Deku). And like mentioned, AFO didn't even realize his brother had a quirk so I'm not sure if AFO knew all this all along. Then again, AFO might just have a gut feeling (or, something) to know every move that Deku makes. (After all, OFA quirk did came from AFO, so...)
And about the case of Monoma, I'm not really sure, but as most people speculated he only get to copy the base quirk of OFA (which is the base version of the quirk, probably combined all the Vestiges' quirks at base form to result something like 5% of OFA: Full Cowl)
And as for Deku trying to show off Black Whip when he literally just got to use the quirk, well...dunno what to say. It's kind of flawed, honestly. (then again it was the cliffhanger of the chapter, we might even see him fail next chapter on using the quirk to an extent)