"Who did eat this cake?" is a possible sentence, but it isn't often said. Here's an example of when it might be used.
Person A: Who ate this cake? Person B: Hmm... Who _did_ eat this cake? (feeling puzzled)
"Did eat" gives the sentence more emphasis. Person B probably wasn't thinking about who ate the cake before, but realized it was an important question when Person A asked, and he is puzzled by it.
"What know you?" is archaic English. In modern English, you normally say "What do you know?"
"Do you not know that?" is a normal sentence, if a bit formal-sounding. "Don't you know that?" is more casual.
In this case I'm afraid Person B is blaming someone for eat that cake. Anyway >"Did eat" gives the sentence more emphasis. I'm on your side. What it emphasizes is another problem.
"What know you?"seems to be no longer a question sentence. I think it means you know nothing at all! to put an emphasis on asking.
>>951 the correct sentence to use if you're trying to say to use 最初のto useいらんだろ
1. It is supposed to ... = It is said to ... e.g.: Let's go and see that movie. It's supposed to be very good. (= It is said to be very good.)
2. Something is supposed to happen. = It is planned, arranged, or expected. e.g.: The train was supposed to arrive at 11:30, but it was an hour late. (= The train was expected to arrive at 11:30 according to schedule.)
3. You're not supposed to do something = it is not allowed or advisable for you to do it. You're not supposed to park your car here. (= You're not allowed to park here.)
>>980 Both of those are natural sentences. "real late" is colloquial, though. Ignore >>981 and >>983. >>982's suggestions are okay. They sound a bit stiff, though.