Please see the P.S.

Maybe I haven't gotten used to this English structure or convention. I may add an 'if' in your sample sentence. as: I want to know IF what the film director says is going to happen if the studio cuts his budget.. But I know I'm probably wrong for that.

@Dan: An if at the head of that clause would render it ungrammatical. It turns what the film director says is going to happen if the studio cuts his budget into a long noun-phrase subject without a main verb. I want to know if what the film director says is going to happen if the studio cuts his budget [involves decapitating a race horse]

It looks to me that "what ... is going to happen" is a complete sentence, instead of noun phrase, like your example: "what the film director says is going to happen if the studio cuts his budget." That's why I was thinking why a complete sentence can be taken as the object of a prep, WITH in this case.

Well, the subject is "what the film director says" and the verb is "happen". Does it make any sense?

As you said it "what [i.e. that which] the planets say is going to happen", can we just remove "which the planets say" and then the sentence becomes "that is going to happen." So do you think if it's ok to say "I want to know IF that's going to happen?" -> "I want to know IF that which you say is going to happen." -> "I want to know IF what you say is going to happen." Does this logic make a bit sense to you?

Change "is going to" to "will" in those sentences and you will see that happen does not bear the tense. What is the finite main verb?

i don't see that makes any difference. Any problem with the sentence "I want to know if that will happen."? Or "I want to know if that, which you say, will happen." Any problems with them?

You are completely departing from the original syntax by using a that-clause instead of an interrogative with what and adding an if. Your syntax is entirely unrelated to the original. what the planets say will happen is a noun phrase or a noun clause. It functions nominally.

Can "what the planets say will happen" be an independent sentence?

@dan: Yes it can, but not as the object of the preposition with.

so are you saying"he was talking about interfering with what the planets say is going to happen" is correct, but "he was talking about interfering with what the planets say will happen" is wrong? is that correct?

@Dan: Not at all. He was talking about interfering with {something}. Something = "what the planets say is going to happen". I only suggested that you change "is going" to "will" when you thought your sentence with "if" was grammatical; it lacked a main verb, and I thought a simpler verb structure might make that clearer to you.

"I want to know if what you are saying will happen." Not: which you say.

but why did you say: "@dan: Yes it can, but not as the object of the preposition with." then?

@dan: because in your question the quotation has with what the planets say is going to happen and so what the planets say is going to happen cannot be parsed as an independent clause. It can be paraphrased "what the planets are making happen". It functions nominally, "that which the planets are making happen".

I think the key confusing point still is that if you take "he was talking about interfering with what the planets say is going to happen" as a noun phase, why can it also be a complete sentence?

@dan. No. No. No. We are not taking that entire sentence nominally, only what the planets say is going to happen. Compare: He was questioning me about what they said was going to happen. He was questioning me about {something}.

@Lambie You added another confusion here because T said adding "if" is incorrect. "I want to know if what you are saying will happen." is a correct sentence? If so, why "I want to know if what the film director says is going to happen..." is wrong?

@Tᴚoɯɐuo Sorry, I typed it wrong in my previous comment. I meant "what the planets say is going to happen". Is it also a complete sentence if I put a dot at the end of it?

@Tᴚoɯɐuo Now I seem to undersand you. Are you saying that we take "what the planets say is going to(or will) happen" as a noun phrase when it's used as the object of WITH. And it could also be a complete sentence or a full clause when it stand alone. Is that correct?