Arlie's analysis analysed.

> 2. þar _kømr_ mest fjölmenni hingat á _Norðurlönd_
>
> kømr: verb (koma); 3rd person, singular, present
> Norðurlönd: noun (Norðurland), neuter, plural, accusative

Correct.
(That was supposed to be 'Norðrlönd'; my mistake.)

> 3. Þorbjörn var auðigr maðr ok var þá gamall,
> er þetta var _tíðenda_.
>
> tíðenda: noun (tíðendi), neuter, plural, genitive

Correct.

> 4. gifti þar _Ólöfu dóttur Þorsteins rauðs_
>
> Ólöfu: proper noun (Ólaf? Ólafa?), feminine,
> singular, accusative
> dóttur: noun (dóttir), feminine, singular, accusative
> Þorsteins: proper noun (Þorsteinn), masculine, singular, genitive
> rauðs: adjective (rauðr), masculine, singular, genitive

Correct. The nominative is 'Ólöf'.

> 5. Þar sat maðr fyrir ok fagnaði _þeim_ vel ok spurði hvat
> þeir _vildi kaupa_.
>
> þeim: pronoun (þeir), masculine, singular, dative
> vildi: verb (vilja), 3rd person, singular, past
> kaupa: verb (kaupa), infinitive, active voice

Two errors here. Think about the meaning.
"A man sat in front and welcomed them".

> Question: Why do we have vildu kaupa in sentence 1
> but vildi kaupa in sentence 5?
>
> The difference between "þeir vildu kaupa" and
> "hann vildi kaupa". (i.e. in the first sentence,
> the subject of the verb is plural, broeðr, and
> in the 5th sentence the subject is singular, maðr.)

You are correct that the singular 3rd person past
indicative active voice is 'vildi' and the plural
3rd person past indicative active voice is 'vildu'
- but that is not the answer here.

> A man is named Eyvindr - he lived in Norway.
> maðr heitir Eyvindr - hann býr í Norðvegi.

Okay. I intended the past tense for 'búa' though.
'Norðvegr' is probably the oldest form of the name
but it is not attested. 'Norvegr' and 'Noregr' are.
This is comparable to English; you say 'Norway'
rather than 'Northway'.

> His brother was called Gunnarr.
> Bróðir sinn heitir Gunnarr.

Again I intended the past tense.

When to use the reflexive pronouns and when
to use the personal pronouns can be a subtle
thing.

"Maðr er nefndr Haukr. Bróðir _hans_ heitir Trausti.
Haukr sér bróður _sinn_. Haukr gefr bróður sínum gjöf."

Generally I don't think 'sinn' is used in nominative.

> The brothers were both big and strong.
> Broeðr váru baðir miklir ok sterkir.

Again not what I intended.

1. Both the brothers were big and strong.
2. The brothers were both big and strong.

To translate the first one I would say:

"Þeir broeðr báðir váru miklir ok sterkir."

But to translate the second one you use
a conjunction. Take a look at week 2's text.

Kveðja,
Haukur