Hún safnar vínylplötum auk þess að semja um verð á flóamarkaðnum.

Safna is the dictionary form, the infinitive, meaning to collect. In the sentence, the verb is conjugated to match hún (she), so it becomes safnar, which is the 3rd person singular present tense.

So:

• að safna = to collect
• hún safnar = she collects

Because safna takes the dative case, not the accusative.

The noun vínylplötur is the nominative plural form (vinyl records as a subject), but after safna you need the dative plural:

• vínylplötur = nominative plural
• vínylplötum = dative plural

This is very important in Icelandic: you often have to learn a verb together with the case it governs.
Here the pattern is:

• að safna einhverju = to collect something

Yes. It is a compound noun, which is extremely common in Icelandic.

It is made from:

• vínyl = vinyl
• plata = record, disc

So vínylplata means vinyl record, and vínylplötum is the dative plural form of that compound noun.

Icelandic often writes compounds as one word where English would use two words.

Auk þess að introduces an additional action, something like besides, in addition to, or as well as.

Grammatically, it connects the main clause with an infinitive phrase:

• Hún safnar vínylplötum = main clause
• auk þess að semja um verð... = additional action

So it works like in addition to doing X or besides doing X.

Because auk normally governs the genitive case.

In the fixed expression auk þess að, the word þess is the genitive form of það. Literally, the phrase is built from something like in addition to that, to..., but in natural English you would not translate it word-for-word.

For learners, it is best to treat auk þess að as a set phrase.

Because after auk þess að, Icelandic uses the infinitive.

So:

• semja = to negotiate / to agree / to compose, depending on context
• semur = negotiates / agrees / composes

Here the structure is:

• auk þess að + infinitive

So að semja is exactly what you expect after this phrase.

Here semja um means to negotiate about, to bargain over, or to agree on something, depending on context.

The preposition um is part of the verbal expression here. Icelandic often uses a verb + preposition combination where English might use a different structure.

So you can think of:

• semja um verð = negotiate about the price / bargain over the price

It is best to learn semja um as a unit when it has this meaning.

Because um takes the accusative, and verð happens to have the same form in the nominative and accusative singular.

So even though the case does change grammatically, the word itself looks the same.

This is common with many neuter nouns in Icelandic.

After á, Icelandic uses:

• dative for location: on / at
• accusative for motion toward: onto / to

Here the meaning is location, at the flea market, so the noun must be in the dative singular:

• flóamarkaður = nominative singular
• flóamarkaði = dative singular indefinite
• flóamarkaðnum = dative singular definite, at the flea market

So á flóamarkaðnum means at the flea market.

The -num ending shows two things at once:

1. dative singular
2. definite article (the)

Icelandic usually attaches the definite article to the end of the noun instead of writing a separate word like English the.

So:

• flóamarkaður = a flea market
• flóamarkaðnum = the flea market, in the dative singular

This kind of combined ending is very common in Icelandic noun forms.

In normal Icelandic, the subject pronoun is usually expressed, so hún is natural and expected here.

Unlike some languages that regularly drop subject pronouns, Icelandic generally keeps them in ordinary sentences unless the context is very special, such as diaries, commands, or certain stylistic situations.

So Hún safnar... is the normal way to say it.

The given word order is very natural:

• Hún safnar vínylplötum auk þess að semja um verð á flóamarkaðnum.

Icelandic word order is somewhat flexible, but changing it usually changes the focus or style, not the core meaning.

For example, moving á flóamarkaðnum earlier could sound more emphatic or marked. For a learner, the version you have is a good standard pattern:

• subject
• finite verb
• object
• additional infinitive phrase

So yes, some variation is possible, but this sentence is already in a very normal order.