Learn Hardcore Icelandic: Hún hittir vinnufélaga sinn við stöðina.

Because hitta takes a direct object in the accusative case. The noun vinnufélagi (coworker; masculine, weak) has accusative singular vinnufélaga, so the object appears as vinnufélaga.

What does sinn mean here, and how is it different from hennar?

sinn is the reflexive possessive for third person; it means “her own” (refers back to the subject).
hennar is the non‑reflexive “her” (refers to some other woman, not the subject). Examples:
Hún hittir vinnufélaga sinn = She meets her own coworker.
Hún hittir vinnufélaga hennar = She meets her coworker (someone else’s).

Does sinn agree with the subject (Hún) or with the noun it modifies?

It agrees with the noun it modifies. Here, vinnufélaga is masculine singular accusative, so the form is sinn (masc. acc. sg.), not sína. Quick guide (accusative):

Masculine sg.: sinn
Feminine sg.: sína
Neuter sg.: sitt
Plural: sína (neuter pl.: sín)

Why isn’t it sínum?

sínum is dative masculine singular. We need accusative to match vinnufélaga (the object), so the correct form is sinn.

Can I omit the possessive and just say she meets a coworker?

Yes. Hún hittir vinnufélaga = “She meets a coworker” (unspecified whose). To say “one of her coworkers,” use the numeral: Hún hittir einn vinnufélaga sinn.

Why is it við stöðina and not við stöðinni?

The preposition við always takes the accusative. The definite feminine accusative of stöð is stöðina. stöðinni is dative, which you’d use after prepositions like á for static location (e.g., á stöðinni = at the station).

What’s the nuance of við here compared to á, hjá, or með?

við (+ acc.): by/next to/at (adjacent to) or against. við stöðina ≈ by the station.
á: “at/on/in.” Static location takes dative: á stöðinni = at the station (on/in the premises). Motion to takes accusative: á stöðina = onto/to the station.
hjá (+ dat.): by/near; also “at someone’s place” or “with (employed by).” hjá stöðinni = near the station.
með: with (accompaniment/instrument), not location: með vinnufélaga sínum = with her coworker.

Why does stöðina have the ending -ina?

It’s the definite article attached to a feminine noun in the accusative singular:

Nominative: stöðin (the station)
Accusative: stöðina (the station, as object or after acc. prepositions like við)
Dative: stöðinni Since við demands accusative, we get stöðina.

Why is the verb hittir (and not, say, hittar or hittur)?

It’s the regular present tense of hitta for 3rd person singular. Present indicative:

ég hitti
þú hittir
hann/hún/það hittir
við hittum
þið hittið
þeir/þær/þau hitta

Could I use hittast, mæta, or kynnast instead of hitta?

hittast (middle/reciprocal): “meet each other.” Þau hittast við stöðina.
mæta (+ dat.): “show up/attend,” or “encounter (face)” rather than a social meet. Not the default for “meet someone.”
kynnast (+ dat.): “get to know; meet for the first time.” Hún kynnist vinnufélaga sínum. For a neutral “meet/see,” hitta is the go‑to verb.

Can the possessive go before the noun (e.g., sinn vinnufélaga)?

Default Icelandic style places possessives after the noun: vinnufélaga sinn. Pre‑posed possessives (e.g., sinn vinnufélaga) are possible but sound marked/emphatic or stylistically non‑neutral. Use the post‑posed order in normal speech.

Is there any article like “a” in Icelandic? Why no word before vinnufélaga?

Icelandic has no indefinite article. Bare nouns can be indefinite. If you want to make the “a(n)” explicit, use einn/ein/eitt (one): einn vinnufélagi, accusative einn vinnufélaga.

The noun vinnufélagi is grammatically masculine. Does that mean the coworker is male?

Not necessarily. Many Icelandic nouns have a grammatical gender that doesn’t match the person’s real‑world gender. vinnufélagi can refer to any coworker, regardless of gender.

How would I say “She meets her coworkers” (plural)?

Hún hittir vinnufélaga sína við stöðina.

vinnufélaga here is accusative plural.
sína is the accusative plural of sinn, agreeing with the plural noun.

Can I change word order for emphasis or to ask a question?

Yes.

Emphasis/fronting: Við stöðina hittir hún vinnufélaga sinn.
Yes/no question (verb-second inversion): Hittir hún vinnufélaga sinn við stöðina?

Any quick pronunciation tips for tricky letters here?

ð in stöðina is like the “th” in “this.”
ö is a rounded vowel, roughly like French “eu” in “bleu.”
Double tt in hittir is a long voiceless [t] sound; stress is always on the first syllable: HÚN hittir, VINN-ufélaga, STÖÐ-ina.