Se la seruro denove ne funkcios, ni petos tiun laboristinon ŝanĝi ĝin morgaŭ.

Esperanto does not follow the English rule that an if-clause normally uses present tense for future meaning. After se, Esperanto can use the tense that matches the time actually meant.

So here:

• Se la seruro denove ne funkcios = if the lock does not work again / if the lock will fail again

Because the possible problem is in the future, funkcios is completely natural.

-os and -us give different shades of meaning.

• -os = a real future possibility
• -us = a more hypothetical or less direct situation

So:

• Se ... ne funkcios, ni petos ... = If it fails again, we will ask ...
• Se ... ne funkcius, ni petus ... = If it were to fail / if it didn’t work, we would ask ...

The sentence as given sounds like a normal plan for a possible future event, so -os fits best.

Denove means again.

In this sentence it goes with ne funkcios, so the idea is:

• if the lock doesn’t work again
• if the lock fails again

Its position is natural because it sits close to the verb phrase it modifies. Esperanto adverbs are fairly flexible, but this placement is clear and normal.

Laboristinon is built from several parts:

• labor- = work
• -ist- = a person associated with an occupation or activity
• -in- = female
• -o = noun
• -n = accusative ending

So laboristino means female worker or woman worker, and laboristinon is that same word in the accusative form.

Because tiun laboristinon is the direct object of petos.

• ni petos tiun laboristinon = we will ask that female worker

In Esperanto, words that go together often agree in case. Since laboristinon has the accusative ending -n, tiun also takes -n.

So:

• tiu laboristino = that female worker
• tiun laboristinon = that female worker, as a direct object

With peti, Esperanto commonly uses a direct object for the person being asked:

• peti iun = to ask someone

So this structure is normal:

• ni petos tiun laboristinon ŝanĝi ĝin
  = we will ask that female worker to change it

This is one of those verb patterns you simply learn as part of the verb’s usage.

Because after peti, Esperanto often uses an infinitive for the action being requested:

• peti iun fari ion = ask someone to do something

So:

• petos tiun laboristinon ŝanĝi ĝin
  = will ask that female worker to change it

The future tense is already shown by petos. The changing is expressed as the action requested, so Esperanto uses the infinitive ŝanĝi.

Esperanto does not need a separate word like English to for the infinitive. The ending -i already means that.

So:

• ŝanĝi = to change
• funkcii = to function
• peti = to ask

That is why ŝanĝi by itself already means to change.

Ĝin refers back to la seruro.

• seruro = lock
• ĝin = it

Esperanto uses ĝi for a thing or non-person. Since the lock is the thing being changed, the sentence uses ĝin.

The -n is there because it is the direct object of ŝanĝi:

• ŝanĝi ĝin = change it

No, not naturally here.

Ĝin most clearly refers to la seruro, because that is the thing that can be changed. The worker is a person, and if you wanted to refer back to her, you would normally use ŝin, not ĝin.

So in this sentence:

• tiun laboristinon = the female worker
• ĝin = the lock

As written, many readers will most naturally connect morgaŭ with ŝanĝi ĝin, so the sense is:

• we will ask that female worker to change it tomorrow

But adverbs can sometimes be a little flexible, so if you want to remove any doubt, word order can help:

• Morgaŭ ni petos tiun laboristinon ŝanĝi ĝin.
  = Tomorrow we will ask that female worker to change it.

• Ni petos tiun laboristinon ŝanĝi ĝin morgaŭ.
  = We will ask that female worker to change it tomorrow.

Yes. Esperanto can also use a ke-clause, for example:

• Ni petos, ke tiu laboristino ŝanĝu ĝin morgaŭ.

That means essentially the same thing. But the infinitive pattern:

• peti iun ŝanĝi ion

is very common, compact, and natural, so the original sentence is an excellent standard way to say it.

Tiu means that one / that specific one, while ĉi tiu means this one.

So:

• tiun laboristinon = that female worker
• ĉi tiun laboristinon = this female worker

The sentence simply chooses that rather than this. That usually means the worker is already known from context or is being identified as a particular person.