S1: I see Law winning tbh.
Anyone else around the same level (Ace, Luffy etc.) and I say BB takes it.
But if this is in character Law would probably merk Blackbeard especially with the conditions you set (Law has intel on BB, BB has none). That favours Law heavily, he knows how to use his brain. Probably a mid diff win with those conditions.
S2: Not sure how this would play out. Teach still has no intel and Law does, once again with a fruit like Law's you need intel, not only that Law knows about Teach's fruit so he will take advantage of that with his tactical ability, the conditions are the only thing keeping BB from winning decisively in this scenario.