Þjónninn var vinalegur, en gesturinn var ókurteis.

It is the definite article, attached to the end of the noun. So:

• þjónn = waiter
• þjónninn = the waiter

and

• gestur = guest
• gesturinn = the guest

In Icelandic, the is usually not a separate word like English the. It is normally added to the noun as an ending.

Because they come from different noun stems and follow slightly different masculine noun patterns.

• þjónn → þjónninn
• gestur → gesturinn

Many masculine nouns in Icelandic have nominative singular forms ending in -ur, like gestur. When the definite article is added, that often becomes -urinn.

So:

• gestur = guest
• gesturinn = the guest

But þjónn already ends differently, so its definite form is þjónninn.

This is very normal in Icelandic: the article is added, but the exact shape depends on the noun class.

Because after var (was), Icelandic uses an adjective, just like English does in sentences such as He was friendly.

So here:

• Þjónninn var vinalegur = The waiter was friendly
• gesturinn var ókurteis = the guest was rude

You are describing what the subject was like, not how someone did an action. That is why an adjective is used.

Because it agrees with the noun it describes.

In this sentence, þjónninn is:

• masculine
• singular
• nominative

So the adjective also appears in the masculine singular nominative form:

• vinalegur

This kind of agreement is very important in Icelandic. Adjectives change form depending on gender, number, case, and whether they are weak or strong.

Not all adjectives use the same endings. Ókurteis belongs to a different adjective pattern.

So even though it is also describing a masculine singular nominative noun, its correct form here is still:

• ókurteis

Compare the idea in English: adjectives do not all have to look alike. In Icelandic, adjectives do change, but different adjectives can follow different patterns.

Ó- often means un-, in-, or not- in English.

So:

• kurteis = polite
• ókurteis = impolite / rude

This is a very useful prefix in Icelandic, and you will see it in many words.

They are in the nominative case because they are the subjects of the two clauses.

• Þjónninn var vinalegur
• gesturinn var ókurteis

In each clause, the noun is the thing being described, so nominative is used.

Because the sentence has two clauses joined by en (but):

1. Þjónninn var vinalegur
2. gesturinn var ókurteis

Each clause needs its own verb, so var appears in both parts.

Yes. En means but and is used to connect contrasting ideas.

So:

• Þjónninn var vinalegur, en gesturinn var ókurteis.
• The waiter was friendly, but the guest was rude.

That comma is also natural here, because two full clauses are being joined.

Yes, but then the meaning changes.

• þjónninn = the waiter
• gesturinn = the guest

Without the definite article, you would have just:

• þjónn = waiter / a waiter
• gestur = guest / a guest

Icelandic does not usually have a separate word for a/an, so the bare noun often carries that indefinite meaning.

Þ is pronounced like the th in think, not like the th in this.

So Þjónninn begins with that voiceless th sound.

A rough pronunciation guide for the first sound is:

• Þj... ≈ thy... / thyoh...

The exact Icelandic pronunciation is more specific, but the key point is that Þ = th as in thin.

This is the most neutral and natural word order:

• Subject + verb + adjective

So:

• Þjónninn var vinalegur
• gesturinn var ókurteis

Icelandic word order can be more flexible than English in some contexts, but this basic order is the standard one learners should be comfortable with first.

Because they are being used predicatively, not attributively.

Compare:

• vinalegur þjónn = a friendly waiter
  (adjective directly before noun)

but

• Þjónninn var vinalegur = The waiter was friendly
  (adjective comes after was)

So in your sentence, the adjectives are not part of the noun phrase; they are describing the subject through the verb var.

The dictionary forms are:

• þjónn = waiter
• vera = to be
• vinalegur = friendly
• en = but
• gestur = guest
• ókurteis = rude / impolite

The form var is the past singular of vera (to be).