Nýi nágranninn er mjög vinalegur og alltaf kurteis.

Because nýi is the form used before a definite noun.

• nýr nágranni = a new neighbor
• nýi nágranninn = the new neighbor

In Icelandic, an adjective before a definite noun usually takes the weak form, and nýi is the weak masculine nominative singular form of nýr.

The ending -inn is the definite article attached to the noun, so it means the.

• nágranni = neighbor
• nágranninn = the neighbor

Icelandic usually puts the onto the end of the noun instead of using a separate word like English does.

It is masculine, singular, nominative.

That is because:

• nágranni is a masculine noun
• it refers to one person, so it is singular
• it is the subject of er, so it is in the nominative case

The adjective nýi matches the noun in gender, number, and case.

Because they are in a different grammatical position.

• nýi comes before the noun and is part of nýi nágranninn
• vinalegur and kurteis come after er and describe the subject

After vera = to be, Icelandic normally uses the predicate adjective form, which is usually the strong form, even if the subject is definite.

So:

• nýi nágranninn = adjective before a definite noun
• nágranninn er vinalegur = adjective after er

That is why you get nýi but vinalegur.

Because Icelandic adjectives do not all decline in exactly the same pattern.

• vinalegur is an adjective whose masculine nominative singular form ends in -ur
• kurteis is an adjective whose masculine nominative singular form is simply kurteis

They are both still agreeing with the same subject: masculine singular nominative. They just belong to different adjective patterns.

Yes, you can think of it that way.

The full version could be:

Nýi nágranninn er mjög vinalegur og er alltaf kurteis.

In natural Icelandic, the second er is often left out because it would just repeat the same verb. So the sentence means:

• The new neighbor is very friendly
• and [he is] always polite

Mjög is an adverb meaning very. It modifies the adjective vinalegur.

So:

• mjög vinalegur = very friendly

Mjög does not change form. It stays the same no matter what noun or adjective it is used with.

Alltaf means always, and here it goes with the understood second er:

og alltaf kurteis = and [is] always polite

So the structure is roughly:

• mjög modifies vinalegur
• alltaf modifies the idea of being polite

In other words, the sentence says the neighbor is very friendly, and that this neighbor is always polite.

Yes, Icelandic has some flexibility, though different word orders can shift the emphasis.

For example:

• Nýi nágranninn er mjög vinalegur og alltaf kurteis.
  Natural and clear: very friendly and always polite

• Nýi nágranninn er alltaf mjög vinalegur og kurteis.
  This can sound more like always very friendly and polite

So the original sentence is a natural way to separate the two ideas a little: very friendly and always polite.

You would use the indefinite noun and the strong adjective form:

Nýr nágranni er mjög vinalegur og alltaf kurteis.

Compare:

• nýr nágranni = a new neighbor
• nýi nágranninn = the new neighbor

So both the adjective and the noun change when you go from indefinite to definite.