I don't find your examples to be following your own rules. "I wonder if that is a fact?" THAT IS A QUESTION. A question displays uncertainty or doubt. "That is a fact." is a statement lacking uncertainty or doubt, which is why THAT is used. "You know that that's going to fall." This is an example of what you are describing. The speaker is telling the listener that "THAT" is going to fall. "You know if that's going to fall?" This is a question asking if "THAT" is going to fall.
that vs. if and whether
I don't find your examples to be following your own rules.
"I wonder if that is a fact?" THAT IS A QUESTION. A question displays uncertainty or doubt.
"That is a fact." is a statement lacking uncertainty or doubt, which is why THAT is used.
"You know that that's going to fall." This is an example of what you are describing. The speaker is telling the listener that "THAT" is going to fall.
"You know if that's going to fall?" This is a question asking if "THAT" is going to fall.