Magistra dicit in bibliotheca non murmurandum esse; nam cum murmuratur, nec legitur nec bene intellegitur.

It breaks down like this:

• Magistra dicit = The teacher says
• in bibliotheca non murmurandum esse = that one must not whisper in the library / that there should be no whispering in the library
• nam = for
• cum murmuratur = when/whenever people whisper / when there is whispering
• nec legitur nec bene intellegitur = people neither read nor understand well / more literally, it is neither read nor well understood

So the whole sentence has:

• a main clause: Magistra dicit
• an indirect statement after dicit
• then a second statement introduced by nam
• inside that second statement, a cum clause

Because Latin commonly uses an indirect statement after verbs of saying, thinking, knowing, and so on.

In English we say:

• The teacher says that...

In Latin, this is often:

• Magistra dicit ... esse

So dicit ... murmurandum esse is the normal Latin way to report what the teacher says.

Here it is a gerundive, not a gerund.

Why?

• It is combined with esse
• It expresses necessity or obligation
• So murmurandum esse means something like must be whispered in form, but because of the negative and the impersonal construction, the real sense is one must not whisper or there should be no whispering

This is the passive periphrastic construction.

Very literally, it means:

• that it is not to be murmured

But that sounds awkward in English. A natural translation is:

• that one must not whisper
• that people should not whisper
• that there should be no whispering

So the idea is prohibition or necessity: whispering is not allowed.

Because the construction is impersonal.

In a normal indirect statement, you often get:

• an accusative subject
• plus an infinitive

For example:

• magistra puerum legere dicit = the teacher says that the boy is reading

But here Latin is not talking about a specific person. It is making a general rule:

• one must not whisper

So there is no expressed accusative subject like aliquem or discipulos. The idea is indefinite and impersonal.

Bibliotheca is in the ablative singular because in with the ablative shows location:

• in bibliotheca = in the library

Compare:

• in + ablative = in/on somewhere
• in + accusative = into somewhere

So:

• in bibliotheca = in the library
• in bibliothecam = into the library

Because this cum is temporal: when or whenever.

So:

• cum murmuratur = when/whenever people whisper

When cum simply gives the time of an action, Latin often uses the indicative.

A learner may expect the subjunctive because cum can also introduce other kinds of clauses, such as:

• since
• although
• more descriptive circumstantial clauses

But here the meaning is straightforwardly temporal, so the indicative fits well.

Formally, murmuratur is 3rd person singular present passive.

But here it is best understood as an impersonal passive:

• murmuratur = there is whispering
• or people whisper

This kind of passive is common with verbs used without a personal subject. English often translates it more naturally with an indefinite subject like people or one.

So cum murmuratur is better understood as:

• when people whisper
• when there is whispering

not as a stiff literal English passive.

Nam means for or because.

It introduces the reason for what comes before:

• The teacher says not to whisper in the library,
• for when people whisper, reading and understanding suffer.

So nam is explaining why the rule exists.

Nec ... nec ... means neither ... nor ....

So:

• nec legitur nec bene intellegitur = neither is it read nor is it well understood

This is the normal way to join two negative ideas in Latin.

You can think of nec as containing the negative already, so Latin does not need an extra non with each verb.

They are both present passive indicative, 3rd person singular:

• legitur = is read
• intellegitur = is understood

Latin often uses passive forms in general statements where English might prefer an active translation with an indefinite subject:

• people do not read
• people do not understand well

So although the forms are passive, an idiomatic English translation may sound more active and general.

You can take the implied subject as something like:

• what one is trying to read
• the text
• or simply a general unstated it

Because each verb has an unstated singular idea behind it, something like:

• the text
• what is being read
• it

Latin does not need to spell that out here. The sentence is making a general point, not focusing on a specific book or passage.

So singular passive verbs work fine.

Grammatically, bene directly modifies intellegitur:

• nec legitur nec bene intellegitur = neither is it read nor is it well understood

So bene belongs especially to intellegitur, not equally to both verbs.

That said, in the overall sense, the whole second half explains that whispering interferes with studying in general.

Yes. A very natural English rendering would be:

• for when people whisper, they neither read nor understand well
• for when there is whispering, people do not read or understand well

That is often the best way to make sense of the Latin, even though the Latin forms themselves are passive or impersonal.