Learn Hardcore Icelandic: Starfsmaðurinn hjálpar okkur að skrá okkur.

Because it belongs to two different verbs. The first okkur is the person being helped by hjálpar (which takes the dative), and the second okkur is the object of að skrá (which takes the accusative). In 1st person plural, the dative and accusative forms happen to be identical (okkur), so you see the same form twice for two different grammatical roles.

What cases are the two okkur, exactly?

After hjálpar: dative (since hjálpa e-m = “help someone” takes dative).
After (að) skrá: accusative (since skrá e-n = “register someone” takes accusative). You can see the difference clearly in the singular: Hann hjálpar mér að skrá mig.

Is the second okkur “reflexive”?

Functionally, yes—it means “ourselves.” But Icelandic only has a special reflexive pronoun sig for 3rd person. In 1st and 2nd person you use the regular object pronouns: mig, þig, okkur, ykkur (not a special reflexive form).

Why can’t we use sig instead of the second okkur?

Because sig is 3rd person reflexive and refers to the subject of the nearest finite clause. In Starfsmaðurinn hjálpar okkur að skrá sig, the sig would refer to Starfsmaðurinn (“to register himself”), which is not the intended meaning.

Can we omit the second okkur and just say … að skrá?

Not if you mean “register us/ourselves.” Skrá is transitive here and wants an object: að skrá okkur. If you want a generic “register,” Icelandic typically uses skrá sig (3rd-person reflexive in a generic sense) or a noun phrase: hjálpar okkur með skráninguna.

What is að here—preposition or something else?

Here að is the infinitive marker (“to” + verb). It introduces the infinitive skrá. It is not the preposition að (“to/at”), which takes the dative and behaves differently. After modal/auxiliary verbs like vilja/mega/þurfa, the infinitive marker is usually dropped: Við viljum skrá okkur.

Why is it hjálpar and not hjálpa?

Agreement. Starfsmaðurinn is 3rd person singular, so the verb is hjálpar. With a plural subject you’d get hjálpa: Starfsmennirnir hjálpa okkur að skrá okkur.

What does the ending -inn in starfsmaðurinn do?

It’s the suffixed definite article: starfsmaður = “employee,” starfsmaðurinn = “the employee.” Icelandic usually attaches the definite article to the noun rather than using a separate word.

Is hjálpa always followed by að before an infinitive?

Yes, when it introduces an infinitive clause: hjálpa e-m að INF (e.g., hjálpa okkur að skrá okkur). With a noun you typically use við or með: hjálpa okkur við/ með skráninguna. The idiom hjálpa til means “help out” and doesn’t take an object in the same way.

Where does the second okkur go inside the infinitive phrase?

It normally follows the infinitive: að skrá okkur. You don’t place it before the verb (að okkur skrá is ungrammatical). You can front other elements in the main clause for emphasis (e.g., Okkur hjálpar starfsmaðurinn …), but the order inside að skrá okkur stays the same.

Can I use við instead of okkur anywhere here?

No. Við is nominative (“we”) and is used for subjects. Both objects here require object forms: dative okkur after hjálpar, and accusative okkur after skrá.

Could I use aðstoða instead of hjálpa?

Yes, but the patterns differ. Aðstoða takes an accusative object: Starfsmaðurinn aðstoðar okkur …. With an activity, Icelandic commonly says aðstoða e-n við að INF or aðstoða e-n við NOUN: Aðstoðar okkur við að skrá okkur / … við skráninguna. Using bare að INF after aðstoða is heard but is less idiomatic for many speakers.

Is the double okkur only because plural forms look the same?

The duplication is required regardless of form because each verb needs its own object. It’s just more visible here because 1st-plural dative and accusative are both okkur. In forms where the cases differ, you still repeat them, e.g., Hann hjálpar mér að skrá mig.

How would this look in the past tense?

Singular subject: Starfsmaðurinn hjálpaði okkur að skrá okkur.
Plural subject: Starfsmennirnir hjálpuðu okkur að skrá okkur.