Senhora, quer que eu lhe marque um corte com a cabeleireira para a próxima semana?

Because the speaker is addressing the woman formally. In European Portuguese, formal address often uses 3rd person singular verb forms, even when talking directly to someone.

So:

• A senhora quer... = formal
• Tu queres... = informal

That is why the sentence has quer.

Portuguese often leaves out subject pronouns when the verb form already makes the meaning clear. Here, Senhora already shows who is being addressed, so quer is enough.

You could think of the full idea as:

Senhora, [a senhora] quer que eu lhe marque...

but repeating a senhora would sound unnecessary.

Because the two actions have different subjects:

• the woman wants
• I book the appointment

When Portuguese has querer plus another action done by a different person, it normally uses:

querer + que + subjunctive

So:

• Quer que eu marque...? = Do you want me to book...?

If the same person does both actions, Portuguese often uses the infinitive instead:

• Quer marcar um corte? = Do you want to book a haircut?

Because after quer que, Portuguese uses the present subjunctive.

• eu marco = indicative, plain statement: I book / I am booking
• que eu marque = subjunctive, used after expressions of wanting, doubt, emotion, etc.

So quer que eu marque literally means something like do you want that I book.

Here lhe means to you / for you, in a formal sense.

So:

• marcar-lhe um corte
• book a haircut for you

It is an indirect object pronoun. It refers to the person receiving the service arrangement, not to the haircut itself.

In European Portuguese, object pronouns often come before the verb in certain environments, especially in subordinate clauses introduced by words like que.

So:

• quer que eu lhe marque... is the normal pattern

This is a very common word order in European Portuguese.

Right. In this sentence, marcar means to book, to schedule, or to arrange an appointment.

This is very common in Portuguese:

• marcar uma consulta = book an appointment
• marcar uma reunião = schedule a meeting
• marcar um corte = book a haircut

Here um corte means a haircut. It is a shortened form of um corte de cabelo.

In a hair-related context, Portuguese often drops de cabelo because it is already understood.

So:

• um corte
• um corte de cabelo

can mean the same thing here.

Com a cabeleireira means with the hairdresser, referring to the person who will do the haircut.

• com = with
• a cabeleireira = the female hairdresser

This focuses on the appointment being with that professional.

Because cabeleireira is the feminine form, meaning female hairdresser.

• o cabeleireiro = male hairdresser / sometimes also the salon in some contexts
• a cabeleireira = female hairdresser

Here the sentence is clearly referring to a woman.

Yes, but the meaning would shift slightly.

• com a cabeleireira = with the hairdresser, focusing on the person
• no cabeleireiro = at the hairdresser’s / at the salon, focusing more on the place or business

So the original sentence is specifically about booking the haircut with the hairdresser.

It means for next week or sometime next week.

It does not give a specific day. It just places the appointment in the following week. The exact interpretation can depend a little on context, but usually it means the upcoming next week.

Portuguese often uses the definite article with time expressions where English does not.

So Portuguese says:

• a próxima semana
• o próximo mês
• o próximo ano

Even though English usually just says:

• next week
• next month
• next year

Yes. A very natural version is:

Senhora, quer que lhe marque um corte com a cabeleireira para a próxima semana?

Portuguese often drops subject pronouns when they are clear from the verb form. Keeping eu can add a bit of clarity or emphasis, but it is not required.

Yes, it is polite and somewhat formal, especially because of:

• Senhora
• the 3rd person verb form quer
• the pronoun lhe

It sounds very appropriate in a professional or customer-service setting in Portugal.

An informal version could be:

Queres que eu te marque um corte com a cabeleireira para a próxima semana?

The main changes are:

• quer → queres
• lhe → te
• usually no Senhora

This would be used with someone you address as tu.

Grammatically, yes, but in Portugal, directly saying você can sound awkward, overly blunt, or even rude in some situations. Polite European Portuguese often prefers:

• no pronoun at all: Quer que lhe marque...?
• or a respectful noun phrase: A senhora quer...?

That is why Senhora, quer... sounds very natural in Portugal.