Learn French: Ne parlez pas fort, le son est trop aigu ! - Do not speak loud; the sound is too high-pitched!

In French, a few specific adjectives can act directly as adverbs when paired with certain verbs. With parler (to speak), you use the adjective fort to mean "loudly". Because it is acting as an adverb here, it is invariable, meaning it never changes form.

Would it be grammatically correct to say Ne parlez pas fortement?

No, it would sound unnatural in this context. For the physical volume of a voice, French uses parler fort (to speak loudly) or parler bas (to speak quietly). The standard adverb fortement is used for abstract intensity or degree, such as recommander fortement (to strongly recommend).

If we were talking about a feminine noun, like la voix (the voice), would fort and aigu change?

Fort would stay exactly the same, because it is an adverb modifying the verb parlez (adverbs are always invariable). However, aigu is a standard adjective describing the noun, so it would need to agree with a feminine noun: la voix est trop aiguë.

Does aigu always mean "high-pitched"?