Mi petas, ke vi ne faru bruon en la nokto.

Ke introduces a subordinate clause, usually translated as that.

So:

• Mi petas = I ask / I request
• ke vi ne faru bruon = that you do not make noise

In English, that is often omitted, but in Esperanto ke is normally kept.

Faru has the -u ending, which is the volitive ending in Esperanto. It is used for commands, wishes, requests, and similar ideas.

Here, ke vi ne faru bruon means something like:

• that you not make noise
• that you should not make noise
• for you not to make noise

Why not the others?

• faras would mean do/are doing, a statement of fact
• fari is the infinitive, to do

Because this is a request about what someone should or should not do, -u is the right form.

Yes, but it is an indirect command or request, not a direct one.

Compare:

• Ne faru bruon! = Don’t make noise!
  Direct command

• Mi petas, ke vi ne faru bruon. = I ask that you not make noise.
  Indirect request

So the -u form appears in both direct and indirect expressions of will, but the tone here is more polite and less blunt.

Because bruon is the direct object of fari.

• bruo = noise
• bruon = noise as the thing being made

In fari bruon, the action is being done to or involving noise, so the noun takes the accusative -n.

Because the sentence is not talking about one specific, already-identified noise. It just means noise in general.

Esperanto has:

• la = the
• no separate word for a/an

So bruon here can feel like:

• noise
• a noise, depending on context

In this sentence, the sense is general: please don’t make noise at night.

In Esperanto, ne normally goes before the word or idea it negates.

So:

• vi ne faru bruon = you should not make noise

Putting ne before the verb is the normal way to negate the action.

Yes, nokte would also be possible.

These are both natural:

• en la nokto = in the night / at night
• nokte = at night, nightly

The version with en la nokto is a little more literally structured around the time period the night.
The version nokte is shorter and more adverbial.

So:

• Mi petas, ke vi ne faru bruon en la nokto.
• Mi petas, ke vi ne faru bruon nokte.

Both are fine.

This is a very common thing in Esperanto. Time expressions often use la where English does not.

For example:

• en la mateno = in the morning
• en la vespero = in the evening
• en la nokto = at night / in the night

So la here does not necessarily mean one specific night. It is just part of a normal way of expressing the time period.

This is an important vocabulary point.

• peti = to ask for, request
• demandi = to ask a question

English uses ask for both ideas, but Esperanto usually separates them.

So here Mi petas... means I request..., not I ask a question...

Examples:

• Mi petas helpon. = I ask for help.
• Mi demandas vin pri tio. = I ask you about that.

Yes. That is also correct and very natural.

Compare:

• Mi petas, ke vi ne faru bruon en la nokto.
• Mi petas vin ne fari bruon en la nokto.

Both mean roughly the same thing: I ask you not to make noise at night.

The first version uses:

• ke
  • a full clause
• -u form: faru

The second version uses:

• vin as the object of petas
• the infinitive fari

Both patterns are common.

Yes, you could also use brui, which means to make noise or to be noisy.

For example:

• Mi petas, ke vi ne bruu en la nokto.

That is also correct.

The version with fari bruon is very transparent for learners because it is literally make noise, much like English.
The version with brui is shorter and a bit more compact.

Both are good Esperanto.