Ég hef verið að hugsa um þetta.

Here is the breakdown:

• Ég = I
• hef = have
  This is the 1st person singular present form of hafa.
• verið = been
  This is the past participle of vera.
• að hugsa = to think / thinking
  In this construction, it works like be doing in English.
• um = about
• þetta = this

So grammatically, the sentence is built something like:

I have been at thinking about this

But in natural English, it is understood as I have been thinking about this.

This is a very common Icelandic way to express an ongoing action over a period of time, similar to the English have been thinking.

The pattern is:

hafa + verið + að + infinitive

So:

• ég hef verið að hugsa = I have been thinking
• við höfum verið að vinna = we have been working
• hann hefur verið að lesa = he has been reading

This construction is especially useful when the action has been continuing recently or over some stretch of time.

In this sentence, að introduces the infinitive hugsa.

The combination vera að + infinitive is a common way to express an action in progress, a bit like English to be doing.

For example:

• Ég er að lesa. = I am reading.
• Ég var að lesa. = I was reading.
• Ég hef verið að lesa. = I have been reading.

So in hef verið að hugsa, the að hugsa part tells you what activity the speaker has been engaged in.

Because the verb hugsa often uses the preposition um when you mean think about something.

So:

• hugsa um eitthvað = think about something

Examples:

• Ég hugsa um þig. = I think about you.
• Við erum að hugsa um framtíðina. = We are thinking about the future.

If you leave out um, the meaning usually changes or the sentence may sound incomplete, depending on context.

The preposition um takes the accusative case, so the word after it must be in accusative.

Here, þetta is the accusative form of this.

A useful thing to know is that for the neuter singular demonstrative, the nominative and accusative forms are both þetta, so the form does not visibly change here.

Examples:

• þetta er gott = this is good
• ég skil þetta = I understand this
• ég hugsa um þetta = I think about this

In this sentence, þetta is a demonstrative pronoun, meaning this.

It stands on its own rather than describing a noun.

So:

• þetta = this
• þessi bók = this book

Compare:

• Ég hugsa um þetta. = I am thinking about this.
• Ég hugsa um þessa bók. = I am thinking about this book.

In your sentence, þetta refers to some situation, idea, or thing already known from context.

Hef is the 1st person singular present tense of the verb hafa = to have.

The present tense forms are:

• ég hef = I have
• þú hefur = you have
• hann/hún/það hefur = he/she/it has
• við höfum = we have
• þið hafið = you have
• þeir/þær/þau hafa = they have

So ég hef verið... literally starts as I have been...

Verið is the past participle of vera = to be.

In this construction, it stays as verið and does not change for person here.

So you get:

• ég hef verið
• þú hefur verið
• við höfum verið

This is similar to English been, which also stays the same in I have been, you have been, they have been.

Yes. That is also correct, but it means something a little different.

• Ég er að hugsa um þetta. = I am thinking about this.
• Ég hef verið að hugsa um þetta. = I have been thinking about this.

The first one focuses on what is happening right now.

The second one suggests that the thinking has been going on for some time, often recently and up to the present.

So if you want the sense of an ongoing process over time, hef verið að hugsa is the better choice.

Very often, yes, but not always in a perfectly one-to-one way.

In many cases, hafa verið að + infinitive corresponds closely to English have been + -ing:

• Ég hef verið að vinna. = I have been working.
• Hún hefur verið að læra. = She has been studying.

However, languages do not match perfectly in every situation. Icelandic sometimes uses other tense choices where English prefers a continuous form, and vice versa. Still, for this sentence, thinking of it as the Icelandic equivalent of have been thinking is a very good starting point.

A rough learner-friendly guide is:

Yehg hev VEH-rith ath HUK-sa um THET-ta

A few notes:

• Ég begins with a sound like yeh.
• hef has an e like in bed.
• verið has a soft ð sound; many learners first approximate it lightly, almost like a very soft th.
• að also ends with ð, again a soft th-like sound.
• hugsa has a u somewhat like German u or French ou, not exactly like English uh.
• þ in þetta is like English th in thin.

Pronunciation varies somewhat by speaker and speed, so it is best to hear native audio alongside the spelling.

You usually place ekki after the finite verb:

• Ég hef ekki verið að hugsa um þetta. = I have not been thinking about this.

That is the normal way to negate it.

You can do the same with related forms:

• Ég er ekki að hugsa um þetta. = I am not thinking about this.
• Ég var ekki að hugsa um þetta. = I was not thinking about this.

In Icelandic yes/no questions, the finite verb typically comes first:

• Hefur þú verið að hugsa um þetta? = Have you been thinking about this?
• Hef ég verið að hugsa um þetta? = Have I been thinking about this?

So the basic change is word order:

• statement: Ég hef verið að hugsa um þetta.
• question: Hef ég verið að hugsa um þetta?

Yes, Icelandic word order is flexible in some contexts, but the normal neutral order here is:

Ég hef verið að hugsa um þetta.

If another element comes first for emphasis or style, the finite verb still usually stays in second position:

• Þetta hef ég verið að hugsa um. = This is what I have been thinking about.

That version gives extra emphasis to þetta.

For beginners, though, it is safest to learn the neutral pattern first.

Yes, very natural.

A native speaker could use Ég hef verið að hugsa um þetta in many everyday situations, for example when introducing an idea, concern, or decision:

• Ég hef verið að hugsa um þetta undanfarið. = I’ve been thinking about this lately.
• Ég hef verið að hugsa um þetta lengi. = I’ve been thinking about this for a long time.

It is a normal, idiomatic way to express sustained thought over time.