¿Le importa si pregunto por la esterilización?

Because le is the indirect object pronoun used for usted or for him/her.

With importar, Spanish usually says something like Does it bother you? using an indirect object pronoun:

• ¿Te importa...? = informal Do you mind...?
• ¿Le importa...? = formal Do you mind...?

So this sentence is either:

• speaking politely to you in the usted form, or
• asking whether he/she minds

In most learner situations, the most likely interpretation is the polite usted version.

Here, importa means something like matters to you or bothers you.

In this structure, importar works a bit like gustar:

• Me importa = it matters to me
• Te importa = it matters to you
• Le importa = it matters to him/her/you formal

So ¿Le importa si...? is a very common way to say Do you mind if...?

Because after si meaning if/whether, Spanish normally uses the indicative, not the subjunctive, when talking about a real possibility.

So:

• ¿Le importa si pregunto...? = correct
• ¿Le importa si pregunte...? = not correct here

The speaker is asking about a possible real action: if I ask...

This is one of the important differences learners notice, because English does not make this distinction in the same way.

Preguntar por usually means to ask about, to inquire about, or sometimes to ask for someone or something.

Compare:

• preguntar algo = to ask something
• preguntar por algo = to ask about something
• preguntar por alguien = to ask for someone / ask after someone

So here:

• pregunto por la esterilización = I ask about the sterilization

The por is important. Without it, the meaning or structure would change.

Spanish often uses the present tense for an immediate or near-future action, just like English sometimes does.

Here, si pregunto means if I ask. It refers to the possible action the speaker is about to take.

So the present tense sounds completely natural.

It is formal, because of le.

If you were speaking informally to a friend, child, or someone you address as tú, you would normally say:

• ¿Te importa si pregunto por la esterilización?

If you are speaking politely to a stranger, client, older person, or in a professional setting, ¿Le importa...? is appropriate.

Yes. A more polite and softer version would be:

• ¿Le importaría si preguntara por la esterilización?

This uses:

• le importaría = conditional
• preguntara = imperfect subjunctive

That combination makes the request sound more tentative and courteous, similar to English Would you mind if I asked...?

So:

• ¿Le importa si pregunto...? = polite
• ¿Le importaría si preguntara...? = even more polite

Spanish often uses the definite article where English might omit it.

Here, la esterilización refers to a specific concept or procedure already understood in context.

Spanish commonly uses the article with nouns like this, especially when referring to:

• medical procedures
• services
• known topics under discussion

So la esterilización sounds natural. Leaving out la would usually sound incomplete or less idiomatic.

Not necessarily. Esterilización can refer to different things depending on context, for example:

• a medical sterilization procedure
• sterilization of equipment
• in veterinary contexts, spaying or neutering

So the exact meaning depends on the situation. The grammar of the sentence stays the same, but the real-world meaning of la esterilización may vary.

Yes, that is also possible, but it is a slightly different structure.

Compare:

• ¿Le importa si pregunto por la esterilización? = Do you mind if I ask about the sterilization?
• ¿Le importa que pregunte por la esterilización? = also possible, but with que + subjunctive

With que, Spanish normally uses the subjunctive:

• que pregunte

Both versions can be natural, but ¿Le importa si...? is especially common and straightforward for Do you mind if...?

Yes. Le can mean:

• to you formal
• to him
• to her

So on its own, ¿Le importa...? does not tell you exactly which one it is. Context tells you.

In a direct conversation, it usually means you formal. In a sentence describing someone else, it could mean him or her.

A very natural less formal version would be:

• ¿Te importa si pregunto por la esterilización?

And in very casual speech, speakers might also choose alternatives such as:

• ¿Pasa algo si pregunto por la esterilización?
• ¿Puedo preguntar por la esterilización?

These are not identical in tone, but they are common ways to express a similar idea. The original sentence is polite and neutral.