Trommarinn bíður í smástund á meðan hún skiptir um streng á fiðlunni.

Because Icelandic usually puts the definite article on the end of the noun.

• trommari = drummer
• trommarinn = the drummer

So -inn here is the suffixed form of the. This is very common in Icelandic.

Bíður is the 3rd person singular present tense of bíða = to wait.

It matches the subject trommarinn, which is singular. In English this can be translated as either:

• waits
• is waiting

Icelandic present tense often covers both simple present and present progressive.

Icelandic often uses í with a time expression to show duration, where English uses for.

So:

• í smástund = for a short while / for a moment

This is a normal idiomatic pattern. It does not mean you should always translate í as in.

Yes, smástund is a normal compound word meaning a short while or a moment.

You may also hear smá stund, and people will understand it, but smástund is a very natural fixed form in expressions like:

• bíða í smástund = wait a moment

So the one-word form is completely standard here.

Á meðan means while or during the time that.

It introduces the clause:

• á meðan hún skiptir um streng á fiðlunni

So the sentence has:

• a main clause: Trommarinn bíður í smástund
• a subordinate time clause: á meðan hún skiptir um streng á fiðlunni

Because skipta um is a set expression meaning to change, replace, or switch out something.

So:

• skipta um streng = change/replace a string

Without um, skipta often has other meanings such as divide, share, exchange, or matter depending on context.

This is one of those verb + preposition combinations you really need to learn as a unit.

Because strengur is the nominative form, but here the word is the object of skipta um, so it appears in the accusative:

• nominative: strengur
• accusative: streng

So skiptir um streng is grammatically correct.

This also shows another important point: Icelandic has no indefinite article. So streng can mean a string even though there is no separate word for a.

Here á means something like on.

A string is understood as being on the violin, not inside it. So:

• strengur á fiðlu = a string on a violin

This may feel a little different from how English sometimes phrases things, but it is very natural in Icelandic.

Because fiðlunni is the dative singular definite form of fiðla = violin.

Breaking it down:

• fiðla = violin
• fiðlan = the violin
• fiðlunni = to/on/in the violin, depending on the preposition and context

After á, Icelandic uses:

• accusative for motion toward/onto something
• dative for location or state

Here the string is located on the violin, so dative is used: á fiðlunni.

Yes. You could say:

Á meðan hún skiptir um streng á fiðlunni bíður trommarinn í smástund.

But notice the word order in the main clause:

• bíður trommarinn

not

• trommarinn bíður

That happens because Icelandic main clauses normally follow verb-second word order. If the subordinate clause comes first, the finite verb of the main clause still has to stay in the second position.