La laboristino ĉe la banko respondas al mia demando.

The ending -ino marks a female person in Esperanto.

• laboristo = a worker, laborer, employee
• laboristino = a female worker, female employee

So la laboristino means the female worker or the woman employee.

It is built from several parts:

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

So labor-ist-in-o literally means something like work-profession-female-noun, or more naturally, female worker.

La is the definite article, meaning the.

• la laboristino = the worker / the female employee
• la banko = the bank

Esperanto has only one definite article: la. It does not change for gender, number, or case.

Ĉe usually means at, by, with, or in the place of, depending on context.

In this sentence:

• ĉe la banko = at the bank

So la laboristino ĉe la banko means the female employee at the bank.

The ending -as shows the present tense in Esperanto.

• respondas = answers / is answering
• respondis = answered
• respondos = will answer

So the sentence is in the present tense.

In Esperanto, respondi normally takes al before the thing or person being answered.

So:

• respondi al demando = to answer a question
• respondi al homo = to answer a person

This is different from English, where we often say simply answer a question without a preposition. In Esperanto, al is the normal pattern here.

Because the phrase is governed by the preposition al.

In Esperanto, a noun after a preposition usually does not take the accusative -n.

So:

• al mia demando = to my question

Since demando is the object of the preposition al, not the direct object of the verb, it stays demando, not demandon.

Also, the possessive mia matches that form:

• mia demando
• not mian demandon

Because there is no direct object here.

The main verb is respondas, and the thing being answered is expressed with al:

• respondas al mia demando

Also:

• ĉe la banko is a prepositional phrase
• la laboristino is the subject

So no word in this sentence needs the accusative ending -n.

Yes, demando means question, and demandi means to ask.

This is an important false friend for English speakers:

• Esperanto demandi = to ask
• English demand = something stronger, like insist on

So in Esperanto:

• demando = question
• demandi = ask

Do not assume it means demand in the English sense.

Yes. In real usage, laboristo/laboristino can refer generally to a worker or employee, depending on context.

Because the sentence says ĉe la banko, a natural translation might be:

• The female employee at the bank answers my question.

So the exact English word may vary a little with context.

Yes, Esperanto word order is fairly flexible, but the given order is the most neutral and natural.

Standard order here is:

• La laboristino = subject
• respondas = verb
• al mia demando = complement

You could move parts for emphasis, for example:

• Al mia demando respondas la laboristino ĉe la banko.

But that sounds more marked or literary. For learners, the original sentence is the best basic pattern.

It most naturally describes la laboristino.

So the meaning is:

• the female worker who is at the bank
• more naturally, the female employee at the bank

It is not usually understood as modifying mia demando.

In Esperanto, stress is always on the second-to-last syllable of a word.

So:

• la-bo-ris-TI-no
• ĈE
• la BAN-ko
• re-SPON-das
• al MI-a
• de-MAN-do

That regular stress system makes pronunciation much more predictable than in English.