Put me down for the Shigaraki's being twins. I don't think there's anything special about the stockpile quirk, just the healthier Older Brother got the full AFO quirk while his weaker Younger Brother got only a piece of it.
As for why their quirks are so powerful, I think it has something to do with everyone with white hair and red eyes having special quirks. Call it a mutation or what have you, but it seems everyone with that combination of hair and eyes has insanely powerful quirks. BUT, that's assuming the Shigaraki's have red eyes. That's why I can't wait for the next season to come out.
As for why AFO gave his brother a stockpile quirk, it's hard to say, but for now I'm willing to believe either AFO reasoned his brother had something or he stole a quirk that could detect quirks and knew something was up. I wouldn't be surprised AFO being unable to steal it would also pique his interest and would want to learn more. Again, this is all basic speculation.
Now, what really has me interested is AFO's obsession with OFA and whether or not he planned the creation of AFO from the very start. Was his endgame always to let it build in power then find a way to steal it once he's satisfied it's strong enough? Could all his interest in quirk singularity be about whether he can control OFA after he finally gains it?
Honestly, If AFO really wanted to stamp out OFA, he'd have done it looong ago. It's even implied he's the one who kills the Users. You can't tell me he severely injures them and just walks away knowing they can pass the quirk to anyone who happens upon them before they die. He's wanted to get his claws on OFA since the beginning.