Ég veit ekki í hvaða orðflokki þetta orð er.

Because í hvaða orðflokki þetta orð er is an embedded question (also called an indirect question), not a direct question.

Compare:

• Í hvaða orðflokki er þetta orð? = direct question
• Ég veit ekki í hvaða orðflokki þetta orð er. = embedded question after Ég veit ekki

In Icelandic, a direct question often has the verb before the subject, but in an embedded question the word order is more like a statement, so the subject þetta orð comes before the verb er.

Because í here takes the dative case.

The noun is orðflokkur (word class / part of speech), and its dative singular form is orðflokki.

With í, Icelandic usually distinguishes between:

• accusative for movement into
• dative for location or being in

Here the idea is that the word is in a certain word class, not that it moves into one, so the dative is used:

• í orðflokki
• í hvaða orðflokki

It can correspond to either what or which in English, depending on context.

In this sentence, English naturally says what word class, but grammatically Icelandic is using hvaða the same way it often uses it for which/what kind of before a noun.

A useful point: hvaða does not change form here. The case is shown by the noun after it:

• hvaða orðflokkur
• í hvaða orðflokki

So even though the whole phrase is dative because of í, hvaða itself stays hvaða.

Because orð is a neuter noun, and þetta is the correct neuter singular form of this.

So the demonstrative has to agree with the noun:

• masculine: different form
• feminine: different form
• neuter singular: þetta

So:

• þetta orð = this word

This is also helpful because orð can look the same in singular and plural in some forms, but þetta shows that the sentence is talking about one word, not several.

Because this is an indirect question, and Icelandic normally does not use að before an indirect question introduced by a question word or phrase.

Here the embedded clause begins with í hvaða orðflokki, so no að is needed.

Compare:

• Ég veit að þetta orð er nafnorð. = I know that this word is a noun.
• Ég veit ekki í hvaða orðflokki þetta orð er. = I don’t know what word class this word is in.

So að goes with a that-clause, not with this kind of embedded question.

That is the normal position in a main clause.

In a simple Icelandic statement, the finite verb usually comes early in the sentence, and ekki commonly follows it:

• Ég veit ekki
• Hann kemur ekki
• Við skiljum þetta ekki

So veit ekki is the normal way to say do not know.

In this phrasing, yes, í is the natural choice because Icelandic treats the word as being in a word class.

So with vera (to be), you naturally say:

• í hvaða orðflokki þetta orð er

Another natural way to express the same idea is with tilheyra (belong to):

• Ég veit ekki hvaða orðflokki þetta orð tilheyrir.

But if you use er, then í is the expected preposition.

Here it is singular.

You are right that orð can be tricky because the form orð can be both singular and plural in some cases. But in this sentence, þetta tells you it is singular:

• þetta orð = this word
• þessi orð = these words

So the sentence is definitely talking about one word.

The direct question would be:

Í hvaða orðflokki er þetta orð?

That is useful to compare with the embedded version:

• direct question: Í hvaða orðflokki er þetta orð?
• embedded question: Ég veit ekki í hvaða orðflokki þetta orð er.

The main change is the position of er. In the direct question it comes before the subject; in the embedded question it comes after the subject.

It breaks down like this:

• Ég = subject
• veit = finite verb
• ekki = negation
• í hvaða orðflokki þetta orð er = embedded question functioning as the object of veit

So the overall pattern is:

I do not know + [embedded question]

That is why the sentence feels like two parts:

1. Ég veit ekki
2. í hvaða orðflokki þetta orð er