In hac schola diligenter laboratur, et temere non respondetur.

This is a very common Latin construction called the impersonal passive.

Instead of naming a subject such as students, people, or someone, Latin can use a passive verb in the 3rd person singular to mean:

• people work
• one works
• work is done
• people do not answer

So:

• laboratur = people work / work is done
• respondetur = people answer / an answer is given

It is passive in form, but in English we usually translate it with an indefinite active subject like people or one.

Because the verbs are being used impersonally.

Latin does not need to say someone, people, or they here. The verb form itself already gives the idea that the action happens in a general way.

So the sentence is not about a specific person. It means something like:

• In this school, people work carefully, and they do not answer rashly
• or more literally, In this school, careful work is done, and rash answering is not done

Both are:

• present tense
• indicative mood
• passive voice
• 3rd person singular

More specifically:

• laboratur comes from laboro, laborare = to work
• respondetur comes from respondeo, respondere = to answer, reply

Because they are present indicative, the sense is general or habitual: this is what normally happens in the school.

Hac schola is in the ablative singular.

After in, Latin uses:

• ablative for location: in = in, in/on
• accusative for motion into: into, onto

Here the meaning is location, not motion:

• in hac schola = in this school

So the ablative is required.

Because hac has to agree with schola in case, number, and gender.

Schola is:

• feminine
• singular
• ablative

So the demonstrative hic, haec, hoc must also be feminine singular ablative:

• nominative feminine singular: haec = this
• ablative feminine singular: hac = in/with/from this

So:

• haec schola = this school
• in hac schola = in this school

They are adverbs. They modify the verbs.

• diligenter = carefully, diligently
• temere = rashly, carelessly, at random

So they tell you how the action is done:

• diligenter laboratur = people work carefully
• temere non respondetur = people do not answer rashly

Both word orders could make sense, but they can suggest slightly different emphasis.

• temere non respondetur strongly links temere with the idea being denied: rashly people do not answer
• non temere respondetur would also mean people do not answer rashly, but it can sound more like not rashly as a contrasted idea

Latin word order is flexible, so placement often affects emphasis more than basic meaning. Here the sentence is neatly balanced:

• diligenter laboratur
• temere non respondetur

That balance is probably part of why the words are arranged this way.

Et simply means and. It joins the two parallel statements:

• In hac schola diligenter laboratur
• temere non respondetur

Latin sometimes can connect ideas without an explicit and, but here et makes the coordination clear and gives the sentence a tidy, balanced structure.

Not here.

Although respondeo can be used with another word showing to whom or to what someone replies, it can also stand by itself in a general sense:

• respondetur = people answer / there is answering

In this sentence the focus is not on whom someone answers, but on how answers are given: not rashly.

It is most naturally understood as a general rule, habit, or custom.

The present indicative in Latin often has this kind of broad meaning, especially in statements like this. So the sentence sounds like a motto or description of normal practice:

• In this school, people work carefully, and do not answer rashly.

Very literally, you could think of it like this:

• In hac schola = in this school
• diligenter = carefully
• laboratur = it is worked / work is done
• et = and
• temere = rashly
• non = not
• respondetur = it is answered / answering is done

That literal wording sounds unnatural in English, but it helps show how the Latin works. A natural English version is something like:

In this school, people work carefully, and do not answer rashly.