Eru álagningarseðillinn og vaxtabæturnar tilbúin?

Because this is a yes/no question. In Icelandic, yes/no questions normally put the finite verb first.

• Statement: Álagningarseðillinn og vaxtabæturnar eru tilbúin.
• Question: Eru álagningarseðillinn og vaxtabæturnar tilbúin?

So the fronted eru is the Icelandic equivalent of English Are ...?

Because the subject is compound: it contains two things joined by og (and):

• álagningarseðillinn = one item
• vaxtabæturnar = another item

Together, they make a plural subject, so the verb must be plural:

• er = is
• eru = are

Even though álagningarseðillinn is singular by itself, the full subject is plural because it means X and Y.

Because Icelandic usually marks definiteness on each noun itself, using a suffix that works like the in English.

So:

• álagningarseðill = a tax notice / tax assessment notice
• álagningarseðillinn = the tax notice

and

• vaxtabætur = interest benefits / interest rebates
• vaxtabæturnar = the interest benefits / rebates

In English, we can often say the X and Y with just one the. In Icelandic, it is very normal for both coordinated nouns to carry their own definite ending if both are definite.

It is a compound noun plus the definite article:

• álagning = assessment / levy / taxation
• seðill = slip, note, notice, form
• -inn = the definite article suffix for masculine singular nominative

So:

• álagningarseðill = tax assessment notice
• álagningarseðillinn = the tax assessment notice

This is very common in Icelandic: long nouns are often built from smaller words joined together.

This word is also a compound:

• vaxta- = from vaxta, a genitive form related to vextir (interest)
• bætur = compensation, benefits, reimbursement

So vaxtabætur literally means something like interest compensation/benefits.

It is plural because bætur is very often used as a plural noun in Icelandic. That means the whole word is treated as plural too:

• vaxtabætur = interest benefits / rebates
• vaxtabæturnar = the interest benefits / rebates

The ending -nar here is the definite article for a feminine plural nominative form.

Because the adjective must agree with the whole subject, not just one noun.

Here the subject is:

• álagningarseðillinn = masculine singular
• vaxtabæturnar = feminine plural

When Icelandic has a mixed-gender compound subject, the usual default agreement is neuter plural. The neuter plural form of tilbúinn is tilbúin.

So:

• masculine singular: tilbúinn
• feminine singular: tilbúin
• neuter singular: tilbúið
• masculine plural: tilbúnir
• feminine plural: tilbúnar
• neuter plural: tilbúin

In this sentence, tilbúin is neuter plural, not feminine singular.

It is neuter plural here.

The form tilbúin can be ambiguous if you look at it by itself, because the same spelling can represent:

• feminine singular
• neuter plural

Context tells you which one it is. Since the adjective refers to two coordinated nouns together, it is functioning as neuter plural in this sentence.

They are in the nominative.

Why?

• álagningarseðillinn og vaxtabæturnar is the subject of the sentence, so it is in the nominative.
• After vera (to be), a predicate adjective like tilbúin is also normally in the nominative.

So this sentence is a good example of standard nominative subject + nominative predicate adjective.

The statement version is:

Álagningarseðillinn og vaxtabæturnar eru tilbúin.

The only difference is word order:

• Eru ... tilbúin? = Are ... ready?
• ... eru tilbúin. = ... are ready.

That is a very common contrast in Icelandic:

• Verb first for yes/no questions
• Subject first for ordinary statements

It can mean both, depending on context.

tilbúinn / tilbúin / tilbúið often means:

• ready
• prepared
• finished and available

In this sentence, it most naturally means something like ready or available yet. The exact English wording depends on the context, but grammatically it is just the ordinary adjective tilbúinn agreeing with the subject.