Klientservo anstataŭigis ĝin sen ke mi devis pagi.

It is a compound noun: klient- + servo = customer service.

Esperanto makes compounds very freely, and they are usually written as a single word. So klientservo feels natural as the name of a department or function. You may also see klienta servo, but klientservo is a compact, very Esperanto-like way to say it.

Anstataŭigis is the past-tense form of anstataŭigi.

It breaks down like this:

• anstataŭ = instead of, in place of
• -ig- = make, cause
• -is = past tense

So anstataŭigi means something like to replace / to swap out.

In this sentence, Klientservo anstataŭigis ĝin means Customer service replaced it.

This is a very common question.

• anstataŭi often means to take the place of or to stand in for
• anstataŭigi often means to replace something

For example:

• Mi anstataŭis la instruiston. = I stood in for the teacher.
• Mi anstataŭigis la malnovan telefonon. = I replaced the old phone.

So in your sentence, anstataŭigis is the more natural choice if the meaning is that the item itself got replaced.

Because ĝin is the direct object form of ĝi.

In Esperanto, direct objects take -n. Here, the thing being replaced is the object of the verb:

• ĝi = it
• ĝin = it, as the direct object

So:

• Klientservo anstataŭigis ĝin = Customer service replaced it

Sen ke means without when what follows is a whole clause with its own subject and verb.

Here the clause is:

mi devis pagi / mi devu pagi

That clause has its own subject, mi, so a full clause is natural.

This is different from just using sen with a simpler phrase. Sen ke is useful when you want to say without X happening or without someone doing X.

Not if you want to keep the meaning exactly the same.

Klientservo anstataŭigis ĝin sen pagi would normally mean Customer service replaced it without paying. The understood subject of pagi would be the same as the subject of the main verb, namely klientservo.

But your sentence means I did not have to pay, so Esperanto uses a full clause:

sen ke mi ... pagi

That makes the subject clear.

Because sen already supplies the negative idea.

So:

• sen ke mi devu pagi = without me having to pay

You do not normally add ne there. If you said sen ke mi ne devu pagi, it would sound confused and could suggest the opposite idea.

A good rule: after sen, the meaning is already negative, so you usually do not add another negative inside unless you truly mean something more complicated.

Many Esperanto speakers would prefer:

Klientservo anstataŭigis ĝin sen ke mi devu pagi.

That is because after sen ke, Esperanto often uses the -u form for something that did not actually take place or is not being presented as a straightforward fact.

So:

• sen ke mi devu pagi = without my having to pay

Your original devis is understandable, but devu is often felt to be more idiomatic here.

Because -u marks mood, not tense.

It does not itself mean present or future. The time is understood from context. Since the main verb is in the past:

• anstataŭigis

the whole situation is understood as past:

• sen ke mi devu pagi = without my having to pay at that time

So even though devu has no past ending, the sentence still clearly refers to a past event.

Because devi is a modal verb, and modal verbs are followed by an infinitive.

So:

• devi pagi = to have to pay
• povis veni = was able to come
• volas helpi = wants to help

That is why you get:

• mi devis pagi
• mi devu pagi

In both cases, pagi stays infinitive.

Not necessarily.

Without la, klientservo can sound like the name of a department or function, much like English customer service. With la, you are more clearly referring to a specific customer-service department already known in the conversation:

• Klientservo anstataŭigis ĝin...
• La klientservo anstataŭigis ĝin...

Both can be possible, depending on context.

Yes. A very natural simpler version is:

Klientservo anstataŭigis ĝin senpage.

Senpage means free of charge.

That version is shorter and very idiomatic. But it shifts the focus a little:

• senpage = the replacement was free
• sen ke mi devu pagi = I did not have to pay

Those are very close in meaning, but not exactly the same in emphasis.