Mesmo que a faculdade fique longe, minha sobrinha não quer deixar de fazer o estágio.

Here mesmo que means even if.

It introduces a concessive idea: something is true or possible, but it does not change the main result.

So the structure is:

• Mesmo que a faculdade fique longe = Even if the college is far away
• minha sobrinha não quer deixar de fazer o estágio = my niece doesn’t want to give up doing the internship

In some contexts, English might use even though, but with mesmo que + subjunctive, even if is usually the best match.

Because mesmo que normally requires the subjunctive.

• fica = present indicative
• fique = present subjunctive

Portuguese uses the subjunctive after expressions like mesmo que when the speaker is talking about:

• possibility
• uncertainty
• hypothesis
• concession

So:

• Mesmo que a faculdade fique longe = Even if the college is far away / ends up being far away

Using fica here would sound wrong in standard Portuguese.

It comes from the verb ficar.

Present subjunctive of ficar:

• eu fique
• você/ele/ela fique
• nós fiquemos
• vocês/eles/elas fiquem

So in the sentence:

• a faculdade fique = the college is / may be

Here ficar means something like to be located or to be situated.

Ficar longe means to be far away or to be located far from something.

Examples:

• A faculdade fica longe. = The college is far away.
• O trabalho fica longe de casa. = The workplace is far from home.

In your sentence, Portuguese does not say explicitly what the college is far from. That is normal. The reference point is understood from context, such as:

• far from home
• far from where she lives
• far from the internship location

Usually, no.

In Brazilian Portuguese, faculdade normally means:

• college
• sometimes university in everyday speech

This is a very common false friend for English speakers.

So:

• a faculdade here is the college/university, not the faculty as in the teaching staff.

Yes, both are possible in Brazilian Portuguese:

• minha sobrinha
• a minha sobrinha

Portuguese often allows a definite article before possessives, but in Brazil it is frequently optional, especially in many everyday contexts.

So both of these sound natural:

• Minha sobrinha não quer...
• A minha sobrinha não quer...

Leaving out the article can sound a bit lighter or more neutral. Including it can sound slightly more emphatic or regional, depending on the speaker.

Sobrinha means niece.

Related words:

• sobrinho = nephew
• tia = aunt
• tio = uncle

So:

• minha sobrinha = my niece

Deixar de fazer is a very common structure meaning:

• to stop doing
• to fail to do
• to not do
• in context, to give up doing

In this sentence, the most natural idea is:

• she doesn’t want to give up doing the internship
• or she doesn’t want to stop herself from doing the internship

So the phrase adds more nuance than simply quer fazer.

Because deixar de + infinitive is a fixed pattern with a specific meaning.

Compare:

• deixar de fazer = to stop doing / fail to do / give up doing
• deixar fazer = to let someone do or, in some contexts, to allow to do

So the de is very important.

For example:

• Ela deixou de estudar. = She stopped studying.
• Ela deixou o filho estudar. = She let her son study.

Those are completely different meanings.

You could say that, but it would not mean exactly the same thing.

• Minha sobrinha quer fazer o estágio = My niece wants to do the internship
• Minha sobrinha não quer deixar de fazer o estágio = My niece doesn’t want to give up doing the internship

The longer version emphasizes that there is an obstacle, but she still does not want to abandon the idea.

So the sentence suggests something like:

• the distance is a problem,
• but she still does not want to miss the opportunity.

Here estágio means:

• internship
• work placement
• sometimes training period

It is not the same as English stage in the theater sense.

This is another common false friend.

So:

• fazer o estágio = to do the internship

Because o estágio refers to a specific internship, probably one already known from the context.

Compare:

• fazer um estágio = to do an internship in general
• fazer o estágio = to do the internship, a particular one

So this sentence suggests that speaker and listener already know which internship is being discussed.

Yes. You can also say:

Minha sobrinha não quer deixar de fazer o estágio, mesmo que a faculdade fique longe.

That means the same thing.

The difference is mostly about focus:

• Starting with Mesmo que... puts the obstacle first.
• Starting with Minha sobrinha... puts the niece and her decision first.

Both are natural.

Yes, in many contexts that would work:

• Embora a faculdade fique longe, minha sobrinha não quer deixar de fazer o estágio.

This is very similar in meaning.

A small difference:

• mesmo que often feels closer to even if
• embora often feels closer to although / even though

But in real usage, they often overlap.

Both require the subjunctive in this kind of sentence.

It can lean either way depending on context, which is part of why the subjunctive is used.

It can mean:

• the college is far, and that does not change her decision
• or the college may be / turn out to be far, and that still will not change her decision

So the sentence is not strongly focused on proving the fact. It is focused on the idea that distance does not matter to her decision.