Gildistíminn og ákvæðið eru í leiguskilmálunum.

Because the subject is a combination of two things joined by og (and):

• gildistíminn = the validity period
• ákvæðið = the provision / clause

Together, they form a plural subject, so Icelandic uses the plural verb:

• er = is
• eru = are

So:

• Gildistíminn er ... = The validity period is ...
• Ákvæðið er ... = The provision is ...
• Gildistíminn og ákvæðið eru ... = The validity period and the provision are ...

The ending -inn is the suffixed definite article, meaning the.

So:

• gildistími = validity period / period of validity
• gildistíminn = the validity period

Icelandic usually adds the to the end of the noun instead of putting a separate word before it.

It is also the suffixed definite article, again meaning the.

So:

• ákvæði = provision, clause, term
• ákvæðið = the provision / the clause

The exact form of the article changes depending on the noun’s gender and form. Here, ákvæði is a neuter noun, so the definite form is ákvæðið.

Because several grammatical pieces are packed into one word.

The dictionary form is:

• leiguskilmálar = rental terms / lease conditions

In the sentence, it appears as:

• leiguskilmálunum = in the rental terms

This form shows:

• plural
• definite (the)
• dative case

So the ending -unum tells you that the noun is dative plural definite.

Because í can take either the accusative or the dative, depending on meaning.

A useful rule is:

• í + dative = location, in
• í + accusative = movement into something, into

Here the meaning is location: the things are in the rental terms. There is no movement. So Icelandic uses the dative:

• í leiguskilmálunum = in the rental terms

The base form is leiguskilmálar.

This is a plural noun meaning something like:

• rental terms
• lease conditions
• tenancy terms

You can think of the forms like this:

• leiguskilmálar = rental terms
• leiguskilmálarnir = the rental terms
• í leiguskilmálunum = in the rental terms

It is plural.

The singular would be leiguskilmáli, meaning a single rental term or lease condition. But in practice, this idea is often used in the plural, because contracts usually contain multiple terms.

So:

• leiguskilmáli = a rental term
• leiguskilmálar = rental terms

The nouns are:

• gildistími — masculine
• ákvæði — neuter
• leiguskilmálar — masculine plural

Gender matters in Icelandic because it affects:

• the form of the definite article
• adjective endings
• some pronouns and agreement patterns

That is why you get different definite endings:

• gildistími → gildistíminn
• ákvæði → ákvæðið
• leiguskilmálar → leiguskilmálunum (here in dative plural definite)

Yes. Icelandic word order is fairly flexible, especially when you want to emphasize a different part of the sentence.

You can say:

• Gildistíminn og ákvæðið eru í leiguskilmálunum.
• Í leiguskilmálunum eru gildistíminn og ákvæðið.

Both are grammatical. The second version puts more focus on where they are found.

Because Icelandic usually expresses the as an ending attached to the noun.

Compare English and Icelandic:

• the validity period = gildistíminn
• the provision = ákvæðið
• in the rental terms = í leiguskilmálunum

So instead of a separate article like English the, Icelandic often uses a suffixed article.

It would be:

• Gildistími og ákvæði eru í leiguskilmálum.

That would mean something like:

• validity period and provision are in rental terms

This sounds less natural in English, but grammatically it shows the indefinite forms:

• gildistími = a validity period / validity period
• ákvæði = a provision / provision
• leiguskilmálum = in rental terms

In the original sentence, the definite forms make it specific:

• the validity period
• the provision
• the rental terms

They are related but not identical.

• ákvæði often means a provision, clause, or specific item in a legal or formal text
• skilmáli means a term or condition

So in a contract context:

• ákvæði can be one specific clause
• leiguskilmálar are the rental terms/conditions as a whole

That is why both can appear in the same sentence without being redundant.

Og is the conjunction and.

It joins the two nouns:

• gildistíminn og ákvæðið

It works very much like English and.

A rough learner-friendly pronunciation guide would be something like:

• Gildistíminn ≈ GIL-di-stee-minn
• og ≈ ok / ogh (the exact sound varies in speech)
• ákvæðið ≈ OU-kvai-thith
• eru ≈ EH-ru
• í ≈ ee
• leiguskilmálunum ≈ LAY-gu-skilm-OW-lu-num

A few things to notice:

• ð is like a voiced th in this
• í is a long ee sound
• Icelandic stress usually falls on the first syllable

This is only approximate, but it can help you begin reading the sentence aloud.