Did All for one give his ability to Tomura?
As of right now, he wasn't given a quirks by all for one.
I'm sure of it because of the characteristics of nomu. All might says that the people who got quirks from all for one lost the ability to talk (later in the 4th season, endeavor fought a speaking nomu, but at the time when all might defeated all for one, it wasn't possible). Shigaraki can still talk. So, we can be sure for now that he is not given any quirks. There's a chance this might go upside down in future though.