Þetta fornafn ruglar hana minna þegar hún sér það í beygingartöflunni.

Because þetta is already doing the job of this, so the noun usually stays without the suffixed definite article.

• þetta fornafn = this pronoun
• fornafnið by itself = the pronoun

In standard Icelandic, a demonstrative like þetta / þessi / þetta normally replaces the article rather than combining with it.

Fornafn is in the nominative singular.

It is the subject of the sentence:

• Þetta fornafn = the thing that is doing the confusing
• ruglar = confuses

So the structure is:

• Þetta fornafn ruglar hana minna
  = This pronoun confuses her less

Because the subject is singular, the verb is also singular: ruglar.

Hana is the accusative form of hún.

It is used because rugla in the sense to confuse someone takes a direct object in the accusative:

• rugla einhvern = to confuse someone

So:

• hún = she
• hana = her

In this sentence:

• Þetta fornafn ruglar hana minna
  literally: This pronoun confuses her less

Yes. Here minna means less.

It is being used adverbially, modifying the verb ruglar:

• ruglar hana minna = confuses her less

This is a very common Icelandic way to express less with a verb.

You can think of it as an unstated comparison:

• less than before
• less than something else
• less in that situation

So the sentence does not need to say exactly less than what; the comparison can be understood from context.

They are both neuter singular forms, but they do different jobs.

• þetta = this
  It points out the noun: this pronoun
• það = it
  It refers back to fornafn

So:

• Þetta fornafn = this pronoun
• þegar hún sér það = when she sees it

The pronoun það is neuter because fornafn is a neuter noun.

Because það refers to fornafn, while hún / hana refers to a female person.

There are two different referents:

• hún / hana = the woman or girl being talked about
• það = the pronoun (fornafn)

In Icelandic, a pronoun that refers back to a noun usually matches the noun’s grammatical gender, not the gender of the English translation.

Since fornafn is neuter, the referring pronoun is það.

Þegar means when and introduces a subordinate clause:

• þegar hún sér það í beygingartöflunni
  = when she sees it in the declension table

This clause gives the situation in which the main statement is true:

• the pronoun confuses her less
• when she sees it in the declension table

So the sentence has:

1. a main clause: Þetta fornafn ruglar hana minna
2. a subordinate clause: þegar hún sér það í beygingartöflunni

Because sjá = to see, and here the form sér is the present tense, 3rd person singular:

• ég sé = I see
• þú sérð = you see
• hann / hún sér = he / she sees

So:

• hún sér það = she sees it

And það is in the accusative here as the direct object of sér. In neuter singular, the nominative and accusative forms are both það, so the form does not change.

It is dative singular with the definite article.

Breakdown:

• beygingartafla = declension table
• beygingartöflunni = the declension table in the dative singular

The preposition í can take either:

• accusative for motion into something
• dative for location in something

Here the meaning is location:

• she sees it in the declension table

So Icelandic uses the dative:

• í beygingartöflunni

That ending shows two things at once:

1. dative singular
2. definite article = the

The base noun is:

• beygingartafla = declension table

Its dative singular without the article is:

• beygingartöflu

With the suffixed article, it becomes:

• beygingartöflunni = in the declension table

This is very typical Icelandic: the definite article is often attached to the end of the noun instead of being a separate word.

The word order is very natural and straightforward.

Main clause:

• Þetta fornafn ruglar hana minna
• subject + verb + object + adverb

Subordinate clause:

• þegar hún sér það í beygingartöflunni
• conjunction + subject + verb + object + prepositional phrase

Nothing especially unusual is happening here. A learner mainly needs to notice:

• the subject comes first in the main clause
• þegar introduces the subordinate clause
• the pronouns change form by case: hana, það

Yes, exactly.

The sentence implies something like:

• the pronoun confuses her less when she sees it in the declension table
• than when she does not see it there
• or less than before

Icelandic often leaves that comparison unstated when it is obvious from context.

So minna does not need an explicit than... phrase in order to sound natural.