Leiðin heim er löng.

Because -in is the definite article attached to the noun.

• leið = way / route / path
• leiðin = the way

Icelandic often puts the at the end of the noun instead of using a separate word like English does.

So in this sentence, leiðin heim means the way home.

Leiðin is feminine singular nominative.

Why?

• The dictionary form is leið, which is a feminine noun.
• It is the subject of the sentence, so it appears in the nominative case.
• The -in ending makes it definite: the way.

So grammatically, leiðin heim is the subject: the way home.

Here, heim is usually best understood as an adverb of direction, meaning something like home or homeward.

It is very common in Icelandic to say:

• fara heim = go home
• koma heim = come home

So leiðin heim is literally something like the way homeward, but in natural English that becomes the way home.

It is not functioning like an ordinary noun here.

This is a very common Icelandic distinction:

• heim = to home / homeward → direction
• heima = at home → location

So:

• Ég fer heim. = I’m going home.
• Ég er heima. = I’m at home.

In Leiðin heim er löng, the idea is directional: it is the route toward home, so heim is the correct form.

Because Icelandic often does not use a preposition where English uses one.

English says:

• the way home
• go home

Not the way to home or go to home.

Icelandic works similarly here:

• leiðin heim
• fara heim

So there is no missing preposition; the phrase is already complete and natural.

Er is the 3rd person singular present form of vera (to be).

Since the subject leiðin heim is singular, Icelandic uses er:

• Leiðin heim er löng.
• literally: The way home is long.

It is just the normal present-tense linking verb, connecting the subject (leiðin heim) with the description (löng).

Because the adjective has to agree with leiðin, which is feminine singular nominative.

The adjective langur (long) changes form depending on gender, number, and case:

• langur = masculine
• löng = feminine
• langt = neuter

Since leið is feminine, the correct form here is löng.

A useful extra point:
after vera (to be), this is a predicate adjective, and predicate adjectives are typically in the strong form. That is why you get:

• Leiðin heim er löng.

If the adjective were placed directly before a definite noun, you would often see a different form, for example:

• hin langa leið heim = the long way home

So löng is exactly right in this sentence.

No. Leið is broader than just a literal road.

Depending on context, it can mean:

• way
• route
• path
• sometimes even something closer to journey or trip

So Leiðin heim er löng could describe:

• a literal route home
• a long trip home
• a long way back home

The exact nuance depends on context.

Yes, that is possible.

Heimleið is a compound noun meaning something like the route home or the way home, so:

• Heimleiðin er löng.

can also work.

The original sentence, Leiðin heim er löng, is very natural and transparent for learners because it is built from common pieces:

• leiðin = the way
• heim = homeward / home

So both are possible, but the version you were given is extremely normal and easy to understand structurally.

This is the normal, neutral word order.

• Leiðin heim = subject
• er = verb
• löng = predicate adjective

One important Icelandic rule is that in main clauses, the finite verb is usually in second position. In this sentence, the whole phrase Leiðin heim counts as the first element, so er comes second.

You can change the order for emphasis, for example:

• Löng er leiðin heim.

That sounds more literary or emphatic, not as neutral as the original.

A rough learner-friendly guide would be:

• Leiðin ≈ LAY-thin
  
  • where ð is like the th in this
• heim ≈ haym
• er ≈ short eh-r
• löng ≈ something like lungk, but with a rounded vowel that English does not really have

A few sound notes:

• ei in Icelandic is often like ay in say
• ð is a voiced th sound
• ö does not have an exact English equivalent
• ng at the end of löng is pronounced differently from English and may sound close to nk

So a rough overall approximation is:

LAY-thin haym er lungk

That is only approximate, but it is a useful starting point.