Clause and noun as subject in a sentence

Question

Can I use both a clause and a noun as the subject of a sentence?

For example:

How the factors interact and their compound impact are not well understood.

I find the meaning is clear but the structure of the sentence seems not valid.

Answer 1

The problem here—if there is one—is comparable to that of a sentence that runs as follows:

The compression of images and arranging words most effectively are of the essence of poetry.

In both instance, the reader understands what is being said but wonders why the author didn't take the opportunity (or make the effort) to bring the dual subject into parallel form. In my example, the parallel design is easy to achieve by changing "the compression of" to "compressing":

Compressing images and arranging words most effectively are of the essence of poetry.

In your example, the author has several ways of bringing the opening words into parallel. For example:

How the factors interact and what their compound impact may be are not well understood.

or:

The factors' interaction and compound impact are not well understood.

or:

The interaction and compound impact of the factors are not well understood.

or:

Experts do not thoroughly understand the factors' interaction or their compound impact.

or (as George Pompidou suggests in a comment above):

It is not well understood how the factors interact and what their compound impact is.

It seems to me that the human preference for parallel structures in writing and speech is quite strong and that a failure to uphold such parallelism can often be traced to a significant external factor. In the case of the sentence you quote, the external factor might be the author's reluctance to have the words is and are appear contiguously in the sentence—a situation that would have occurred if the author had followed "How the factors interact" with its natural matching form "what their compound impact is":

How the factors interact and what their compound impact is are not well understood.

But the author's decision to take the dual subject out of parallel form in order to avoid the "is are" result was not dictated by necessity; it more likely represented the first avoidance method that the author found at hand.

Aesthetic preference is a matter rather far afield from core considerations of grammar and popular usage, but I think that it is important to recognize that language patterns and choices can have nonrational effects, much as music patterns and choices can. Your conclusion that "the meaning is clear but the structure of the sentence seems not valid" sounds to me like an objection to the aesthetic effect of the author's yoking of subjects expressed in somewhat dissimilar forms. Objectively the sentence is valid, and the author has every right to combine the two forms in a single subject; but subjectively you, as a reader, have every right to dislike the result.

Answer 2

No, neither one. Here is a clause: "The man runs". Here is what happens when I try to use it as a subject: *"The man runs surprises us." No good.

Here is a noun: "man". Here is what happens when I try to use it as a subject: *"Man runs." No good.

For a subject, you need a noun phrase. You can make a noun phrase from the noun "man" by adding a determiner: "The man runs." You can also make a noun phrase from a clause by adding a complementizer: "That the man runs surprises us."

In some cases, nothing needs to be added to a noun to make a noun phrase which works as a subject: "Men run." Nonetheless, "men" in this sentence is a noun phrase.

In your example, "How the factors interact and their compound impact are not well understood", both "how the factors interact" and "their compound impact" are noun phrases, so they can be conjoined to form a noun phrase, which can then be a subject. No problem. The fact that these two noun phrases have different derivations is not relevant to whether they can be conjoined.