Umsögnin um fyrirtækið er góð.

Because Icelandic usually puts the definite article on the end of the noun instead of using a separate word like the.

• umsögn = review / comment / assessment
• umsögnin = the review

Here, -in is the definite ending for this feminine singular form.

The base form is fyrirtæki, which means company.

• fyrirtæki = company
• fyrirtækið = the company

The ending -ið is the definite article for a neuter singular noun in this form. So just like umsögnin means the review, fyrirtækið means the company.

It is in the accusative case, because the preposition um normally takes the accusative when it means about.

So:

• um = about
• um fyrirtækið = about the company

This is a very common thing to memorize in Icelandic: certain prepositions regularly govern certain cases, and um is one of the accusative ones.

Because góð agrees with umsögnin, not with fyrirtækið.

The subject of the sentence is umsögnin um fyrirtækið (the review about the company). The head noun there is umsögn, which is a feminine singular noun. Predicate adjectives after vera (to be) agree with the subject in gender and number, so you get:

• feminine singular: góð
• neuter singular: gott
• masculine singular: góður

So góð is correct because umsögn is feminine.

Because this adjective is being used predicatively after the verb er.

In Umsögnin um fyrirtækið er góð, the adjective comes after to be and describes the subject. In that position, Icelandic normally uses the adjective in the nominative form that agrees with the subject:

• umsögnin ... er góð

Even though the subject is definite (the review), the adjective does not become góða here. Góða would be a different case/form and would not fit this sentence.

It goes with umsögnin.

So the structure is:

• Umsögnin um fyrirtækið = the review about the company
• er góð = is good

That means the sentence is talking about a review, and that review is about the company. The phrase um fyrirtækið is not describing góð; it is specifying which review we mean.

Yes. This is a very normal sentence pattern:

• subject: Umsögnin um fyrirtækið
• verb: er
• complement: góð

So literally the structure is:

• The review about the company
  • is
    • good

This is straightforward, standard Icelandic word order for a simple statement.

Yes, fyrirtækið is definitely singular definite: the company.

The tricky part is that the bare form fyrirtæki can be singular or plural depending on context:

• fyrirtæki = a company or companies
• fyrirtækið = the company
• fyrirtækin = the companies

So in this sentence, the definite ending makes it clear that it means the company, singular.

Not if you want the same meaning.

• umsögn um fyrirtækið = a review about the company
• umsögn fyrirtækisins = the company’s review / the review belonging to the company

Those are not the same idea. In your sentence, um fyrirtækið means the review is about the company. A genitive phrase would more likely suggest that the review comes from the company or belongs to it.

So um fyrirtækið is the right choice for about the company.