Can "What" or "Which" be used as demonstrative pronouns?

Can what or which be used as demonstrative pronouns (this, that, those)?

Instead of

What colors are you using to paint the waterfall and how are you using those colors?

is the following also grammatically correct?

How are you using what colors to paint the waterfall?

Instead of

What information are marketers trying to convey in the advertisement and how are they trying to convey that information?

is the following also grammatically correct?

How are marketers trying to convey what information in the advertisement campaign?

Your two suggestions could be grammatical only if what/which were used as head of an embedded question in the main question. There are specific cases where the question word can be part of a noun phrase which plays two roles in the sentence. Consider:

How are you choosing what/which colors to paint the waterfall with?

The NP what colors is head of the object clause expressed by an embedded question (The direct version of it would be: With what/which colors should you paint the waterfall?). At the same time, the NP what colors is the object of the preposition with.

How are marketers choosing what/which information to convey in the advertisement campaign?

Here the embedded question is: what/which information should they convey in the advertisement campaign?

Your re-writing suggestions of the two original questions are ungrammatical because there are very special cases where you can ask two different questions in the same clause [Who does what? Which should we put where?].

You cannot always combine two questions into one just because their verbs have the same object. You can however avoid repetition by using parallelism:

What colors are you using to paint the waterfall, and how?

What information are marketers trying to convey in the advertisement, and how?

Note that you still have 2 independent questions in one sentence connected by and.

It is true that in some constructions what approaches the use of demonstrative pronouns, especially in sentences where it can be replaced by that which, but this does not occur in questions, whether direct or indirect, but rather in object clauses. Among other meaning of the pronoun what AHD mentions:

That which; the thing that:

• Listen to what/that which I tell you. [the clause what I tell you is the object of the preposition to]

Here is an example with a direct object clause:

I know what/that which you are going to say.