La propietaria quiere resolver la queja hoy mismo.

Because propietaria is the feminine form of propietario. It means female owner or, in some contexts, landlady. The article la also has to match the gender of the noun.

• el propietario = the male owner
• la propietaria = the female owner

In this sentence, the speaker is referring to a woman.

Propietaria literally means owner. Depending on context, it could refer to:

• the owner of a flat or house
• the owner of a business
• a landlady

Without more context, it simply means the female owner.

In Spanish, when one verb is followed by another in the infinitive, you usually do not add a word like English to between them.

So:

• quiere resolver = wants to resolve
• literally: wants resolve

This is a very common structure:

• quiero comer = I want to eat
• necesita salir = he/she needs to leave
• prefieren esperar = they prefer to wait

Resolver means to resolve, to solve, or to sort out. With la queja it means dealing with the complaint and bringing it to a conclusion.

So in this sentence, it is not just listen to the complaint, but more like fix the issue / settle the complaint.

Spanish often uses the definite article when referring to something specific that is already known in the situation.

So la queja suggests the complaint: a particular complaint that both speaker and listener know about, or that has already been mentioned.

If it were una queja, it would sound more like a complaint, meaning a non-specific one.

• resolver la queja = resolve the complaint
• resolver una queja = resolve a complaint

Hoy mismo adds emphasis. It means something like:

• today itself
• today, no later
• right today
• this very day

So hoy just means today, but hoy mismo stresses urgency or immediacy.

Compare:

• Quiere resolver la queja hoy. = She wants to resolve the complaint today.
• Quiere resolver la queja hoy mismo. = She wants to resolve the complaint today itself / today without delay.

Yes, mismo often means same, but it also has an emphatic use. In expressions like hoy mismo, it strengthens the time expression.

Examples:

• ahora mismo = right now
• hoy mismo = today itself / today without delay
• esta misma tarde = this very afternoon

So here mismo is not really same in the usual sense. It is adding emphasis.

This is the most neutral, standard Spanish word order:

subject + verb + object + time expression

• La propietaria = subject
• quiere resolver = verb phrase
• la queja = object
• hoy mismo = time expression

Spanish word order is more flexible than English, but this version sounds natural and straightforward.

You could move parts around for emphasis, for example:

• La propietaria quiere resolver hoy mismo la queja.
• Hoy mismo quiere resolver la queja la propietaria.

But the original sentence is the most neutral and easiest version.

Yes. Depending on context, resolver la queja could be understood as:

• resolve the complaint
• deal with the complaint
• sort out the complaint

Resolve is the closest direct match, but in natural English other translations may sound more normal depending on the situation.

In Spain Spanish, queja is pronounced roughly like KE-ha.

A few useful points:

• qu before e makes a k sound
• the u is silent here
• j in Spanish is a strong throaty sound, not the English j

So:

• queja → KE-ha

It is pronounced roughly:

pro-pye-ta-RYA

A few helpful points:

• ie often sounds like ye
• the stress is on ta
• the final ria sounds together, roughly rya

So you will hear something close to:

pro-pye-ta-RYA

Yes. Since la queja is a feminine singular direct object, you can replace it with la.

So:

• La propietaria quiere resolver la queja hoy mismo.
• La propietaria quiere resolverla hoy mismo.

Both are correct. The second one means The owner wants to resolve it today itself.

Notice that with an infinitive, the pronoun can be attached to the end of the infinitive:

• resolverla

Quiere is the present tense of querer, so it means wants.

• quiere = wants
• quería = wanted / used to want / was wanting
• querrá = will want

So this sentence is talking about a current intention in the present.

Yes, propietaria is completely normal in Spain. It sounds fairly standard and somewhat formal.

In housing contexts, you might also hear:

• la dueña = the owner
• la casera = the landlady

But la propietaria is a very good, clear, standard choice, especially in formal or neutral Spanish.