Learn Hardcore Turkish: Kütüphanede ne fısılda ne de telefonla konuş; herkes çalışıyor. - Neither whisper nor talk on the phone in the library; everyone is studying.

It’s the Turkish correlative conjunction meaning “neither … nor.” It negates both items that follow it. Here, it tells the listener to do neither of the two actions mentioned.

Why are the verbs in the affirmative imperative (fısılda, konuş) instead of the negative imperative (fısıldama, konuşma)?

With ne … ne de, the negation is carried by the conjunction itself, so the verbs stay in their affirmative forms. Using negative imperatives would be a kind of double negation and sounds wrong or at least very awkward here.

Natural: Ne fısılda ne de telefonla konuş.
Unnatural: Ne fısıldama ne de telefonla konuşma.

Can the second part be ne da instead of ne de?

No. In this fixed construction the second element is always written as separate de, not da and not te/ta. Think of it as a set phrase: ne … ne de.

Could I say the same thing using regular negative imperatives instead of ne … ne de?

Yes, a common alternative is to list two prohibitions:

Kütüphanede fısıldama ve telefonla konuşma. This is perfectly natural on signs and announcements. The ne … ne de version sounds a bit more pointed or stylistically emphatic.

What does Kütüphanede express exactly?

It’s the locative case “in/at the library.” Formally: kütüphane + -de (locative). Turkish uses case suffixes instead of separate prepositions like “in/at.”

Does Kütüphanede have to be at the beginning?

No, but placing it first is the most natural way to set the scene. Other positions are possible, but moving it later can sound marked or slightly awkward in a short command. The fronted location here reads like “In the library, …” for emphasis.

Why is it telefonla konuş and not telefonda konuş?

telefonla konuşmak is the canonical way to say “to talk on the phone” (literally, “talk with/by means of the phone,” using the instrumental -la/-le).
telefonda konuşmak is also heard and understood (“speak on the phone”), focusing more on the setting “on the phone.” In prohibitions, telefonla konuş is more idiomatic, but both are acceptable in everyday speech.

What person/number are fısılda and konuş addressing?

They are second-person singular imperatives (talking to one person informally). To address multiple people or be polite, use the plural imperative:

Kütüphanede ne fısıldayın ne de telefonla konuşun. Many speakers prefer the straightforward negatives in the plural: Kütüphanede fısıldamayın, telefonla da konuşmayın.

Where does lütfen (“please”) go to soften the command?

You can place it at the beginning or right after the location phrase:

Lütfen kütüphanede ne fısılda ne de telefonla konuş.
Kütüphanede lütfen ne fısılda ne de telefonla konuş. Lütfen usually comes early in the sentence.

What is the role of the semicolon before herkes çalışıyor?

It separates two closely related independent clauses: the prohibition and the reason. A period would also work. You could also make the reason explicit:

Kütüphanede ne fısılda ne de telefonla konuş; çünkü herkes çalışıyor.
Kütüphanede ne fısılda ne de telefonla konuş. Herkes çalışıyor.

Why is it herkes çalışıyor and not herkes çalışıyorlar?

Herkes (“everyone”) is grammatically singular in Turkish, so it takes a third-person singular verb: çalışıyor. Using a plural verb with herkes is nonstandard; if you want a plural feel, use onlar or rephrase with hepsi:

Herkes çalışıyor. (standard)
Hepsi çalışıyor. (also standard)
Herkes çalışıyorlar. (avoid in standard usage)

Could I express the opposite idea (“Either whisper or talk on the phone”)?

Yes, use the correlative for alternatives:

Ya fısılda ya da telefonla konuş. (Either … or …)