Learn Hardcore Portuguese (Portugal): Há muito desemprego na minha área; no entanto, este estágio pode abrir portas. - There is a lot of unemployment in my field; however, this internship can open doors.

In European Portuguese, há is the normal, standard way to say there is / there are, both in writing and speech.
You could also say existe muito desemprego, but that sounds a bit more formal or emphatic.

In Brazilian Portuguese, people very often say tem muito desemprego in speech, but in Portugal, tem in this sense (there is/are) is much less common and can sound regional or informal.

Why is it muito desemprego and not muitos desempregos?

Because desemprego is being used as an uncountable noun, like unemployment in English. We don’t normally say unemployments in English either.

muito desemprego = a lot of unemployment (mass/uncountable)
muitos desempregados = many unemployed people (countable individuals)

If you want to count people, you change the noun (to desempregados). If you talk about the general phenomenon/level, you keep desemprego singular and uncountable with muito.

Why is there no article before desemprego (why not o desemprego)?

With abstract or uncountable nouns used in a general sense, Portuguese often omits the article, especially after há/existe:

Há muito desemprego na minha área.
Há muita pobreza no país.

You can say O desemprego é um problema sério (with article) when the noun is being treated as a more specific, known concept (here, unemployment as a subject you’re talking about).

But in Há muito desemprego, we’re talking about an indefinite amount of unemployment, so no article is more natural.

What exactly does na minha área mean – is it geographical area or professional field?

Área can mean both in Portuguese, and context decides which it is.

Geographical: na minha área = in my region / in my local area.
Professional: na minha área = in my field (of work/study), e.g., marketing, engineering, etc.

In career or study contexts, minha área is very commonly understood as my professional/academic field, not physical space.

How is na formed, and why is it na minha área and not no minha área?

Na is a contraction of em + a:

em + a área → na área
em + o setor → no setor

Because área is feminine (a área), you must use na.
If the noun were masculine, you would use no:

na minha área (feminine)
no meu setor (masculine)

What does no entanto literally mean, and how is it used?

Literally, no entanto is em + o entanto, but as a fixed phrase it works like however / nevertheless. It’s a formal connector, mostly used in writing or careful speech.

It usually appears after a pause and followed by a comma:

…; no entanto, este estágio pode abrir portas.
Estava cansado; no entanto, continuou a trabalhar.

In everyday informal speech, people more often use mas (but) or só que (but/except that) instead of no entanto.

Why is there a semicolon before no entanto instead of a comma or a full stop?

The semicolon here separates two closely related clauses:

Há muito desemprego na minha área;
no entanto, este estágio pode abrir portas.

You could also write:

Há muito desemprego na minha área. No entanto, este estágio pode abrir portas. (full stop)

Using just a comma before no entanto is common in informal writing, but in standard written Portuguese, a semicolon or full stop is preferred before such connectors.

What is the difference between no entanto, porém, contudo, and mas?

All can translate as but / however, but they differ in style and frequency:

mas – most common, neutral, used everywhere in speech and writing.
no entanto – more formal, typical of written texts, essays, reports.
porém – also formal/bookish, frequent in writing, not so much in casual speech.
contudo – quite formal and literary; you’ll see it in essays, articles, and official texts.

In everyday conversation, people overwhelmingly use mas. The sentence could become:

Há muito desemprego na minha área, mas este estágio pode abrir portas.

Why is it este estágio and not esse estágio?

In traditional European Portuguese usage:

este = this, something close to the speaker (physically, or just now being introduced).
esse = that, something closer to the listener or just mentioned previously.
aquele = that over there, more distant.

Here, este estágio refers to the internship that the speaker is focusing on right now, so este (this) is natural.

In modern everyday speech, especially in Brazil, there’s some mixing of este and esse, but in European Portuguese, este estágio here sounds fully natural and slightly more careful/standard.

What does estágio mean in European Portuguese? Is it always an internship?

In European Portuguese, estágio almost always refers to an internship / work placement / practical training period, usually connected to studies or early career:

university internship
professional training placement
probationary training after finishing a degree

It’s not the stage of a theatre; that would be palco. So in this sentence, este estágio is clearly this internship / training placement.

What does the expression abrir portas mean?

Abrir portas is an idiomatic expression meaning to create opportunities, to open up possibilities (usually for the future, career, contacts, etc.).

Examples (translated):

Este curso pode abrir muitas portas. – This course can open many doors.
Conhecer aquela pessoa abriu-me muitas portas. – Meeting that person opened many doors for me.

It doesn’t mean literally opening physical doors in this context; it’s about opportunities becoming available.

How would the meaning change if we said Este estágio vai abrir portas instead of pode abrir portas?

pode abrir portas = can / may open doors – it’s possible, but not guaranteed; it’s hopeful but cautious.
vai abrir portas = is going to open doors – much stronger, almost a prediction or certainty.

Using pode here fits the realistic tone: there is a lot of unemployment, but this internship might help, without promising too much.

Why is it minha área and not o meu área or meu área?

Because área is a feminine noun (a área), so the possessive must agree in gender:

Feminine: a minha área → na minha área
Masculine: o meu curso → no meu curso

You never say o minha área or meu área; the article and the possessive both match the feminine noun: a minha área.