"J'éspère que vous allez très bien"

Question

Why is "que" used in the sentence above rather than "ce que", despite "vous allez très bien" seems much like a fact(though it is a wish)?

Accepted Answer

Que can be used in several different contexts and come in different grammatical flavors. It can be a relative pronoun (with or without ce) and also a conjunction, starting a relative clause.
Starting with que as simple relative pronoun:
Mon père me raconte des histoires, que j'aime. -- My father tells me stories, that I love.
Que refers to the particular stories, which the father tells her.
Ce que, on the other hand,  refers to an abstract idea, often mentioned in a different sentence, and not to a specific noun in the same sentence.
Mon père me raconte des histoires, ce que j'aime. -- My father tells me stories, which is what I love. 
Que can also start a new relative clause:
J'espère que tu vas bien. -- I hope that you're well.
In this case, que does not refer to any noun.

Answer

And the same case with the sentence: "Ça fait 30 minutes qu'on attend notre table."

Answer

Yes.