Steinninn er harður.

Because Icelandic usually puts the definite article, meaning the, onto the end of the noun. So:

• steinn = stone / a stone
• steinninn = the stone

That attached article is one of the first big differences from English.

Because the noun steinn already ends in -nn, and the definite ending added here is -inn. When you combine them, you get steinninn.

So the spelling is basically showing both parts:

• steinn
  • -inn = steinninn

No, Icelandic does not normally use a separate indefinite article the way English does. So steinn can mean a stone or just stone, depending on context.

That means Icelandic handles articles like this:

• no special word for a/an
• a suffix on the noun for the

Er is the present tense singular form of vera, which means to be. In this sentence it means is.

So:

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is

Since steinninn is singular, er is the correct form.

Because Icelandic adjectives must agree with the noun they describe in gender, number, and case. Here, steinninn is:

• masculine
• singular
• nominative

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

That is a very common question. In this sentence, harður is a predicate adjective: it comes after er and describes the subject. Predicate adjectives in Icelandic normally use the strong form, not the weak definite-style form.

So:

• harði steinninn = the hard stone
  
  • adjective before the noun, attributive use
• steinninn er harður = the stone is hard
  
  • adjective after er, predicate use

So even though the noun is definite, harður is still correct here.

Steinninn is in the nominative case, because it is the subject of the sentence. Yes, harður matches it: it is also nominative, as well as masculine singular.

So the grammar lines up like this:

• steinninn = masculine singular nominative
• harður = masculine singular nominative

In this simple sentence, yes. It follows the basic pattern:

• subject: Steinninn
• verb: er
• complement: harður

So it looks very similar to English: The stone is hard. Icelandic can change word order more than English in some contexts, but this is the normal neutral order for a plain statement.

The noun, verb, and adjective would all change:

• Steinarnir eru harðir. = The stones are hard.

Here:

• steinninn → steinarnir
• er → eru
• harður → harðir

This is a good example of how Icelandic often shows agreement in several words at once.