Hún tekur mynd af plakatinu svo hún muni hvenær næstu tónleikar eru.

There isn’t one. Icelandic has no indefinite article, so a bare noun can mean a/an from context.

• tekur mynd = takes a picture
• myndin = the picture

So mynd by itself can naturally mean a picture.

Because taka mynd af e-u is the normal Icelandic pattern for to take a picture of something.

• tekur mynd = takes a picture
• af plakatinu = of the poster

Here af is part of the expression that tells you what the picture is of.

Two things are going on:

• af takes the dative case
• -inu is the suffixed definite article for a neuter singular noun in the dative

So:

• plakat = poster
• plakati = poster (dative)
• plakatinu = the poster (dative)

That is why you get af plakatinu.

Here svo means so that. It introduces the purpose of taking the picture.

So the structure is:

• Hún tekur mynd af plakatinu = main action
• svo hún muni... = purpose/result intended by that action

You may also see svo að with a very similar meaning.

muni is the present subjunctive of muna (to remember).

• hún man = she remembers (indicative)
• hún muni = she remember / may remember (subjunctive form)

After svo in a purpose clause, Icelandic often uses the subjunctive. So svo hún muni means something like so that she will remember or so that she may remember.

Also, this muni comes from muna (remember), not from the future auxiliary munu.

Because svo hún muni... is a full subordinate clause with its own finite verb, and finite clauses normally need an explicit subject in Icelandic.

So even though the subject is the same person as in the main clause, Icelandic still says:

• Hún tekur... svo hún muni...

A different construction could avoid the repeated pronoun, for example with an infinitive:

• ... til að muna ...

But this sentence uses a full purpose clause instead.

Because this is an indirect question, not a direct question.

Compare:

• Direct question: Hvenær eru næstu tónleikar?
• Indirect question: ... hvenær næstu tónleikar eru

In embedded questions, Icelandic normally uses statement-style word order, so the subject comes before the verb.

Because tónleikar is normally a plural noun in Icelandic. Even when English would say the concert, Icelandic often uses tónleikar and treats it as plural grammatically.

That is why the verb is also plural:

• næstu tónleikar eru...
• literally: the next concerts are...
• natural English: the next concert is...

The adjective has to agree with the noun.

• tónleikar is plural
• so the adjective must also be plural: næstu

This weak form of næsti is the normal one when it means the next in a specific sense. So næstu tónleikar means the next concert / the upcoming concert.

Because tónleikar is grammatically plural, the whole phrase is plural in Icelandic even if English translates it more naturally with singular concert.