Eftir úttektina fór hún aftur inn og gerði litla innborgun.

Because úttekt is a feminine noun, and here it is:

• definite: the withdrawal / audit / inspection
• accusative singular: because in this sentence eftir means after, and with that meaning it takes the accusative

So:

• úttekt = withdrawal / audit / inspection
• úttektina = the withdrawal / audit / inspection

The ending -ina is the definite accusative singular ending for this noun.

This is because Icelandic follows the V2 rule very often: the finite verb tends to come in the second position of the clause.

Here, the sentence begins with Eftir úttektina. That whole phrase counts as the first element, so the verb comes next:

• Eftir úttektina = first element
• fór = second-position verb
• hún = subject

So Eftir úttektina fór hún... is normal Icelandic word order.

If the sentence started with the subject instead, then you would get:

• Hún fór aftur inn...

Fór is the past tense of fara, which means to go.

In this sentence, it is 3rd person singular past:

• fara = to go
• fór = went

So fór hún means she went.

A useful thing to remember is that Icelandic past-tense forms are not always built the way English learners expect. fara is not a regular verb, so you just have to learn fór as its past form.

Because they do slightly different jobs:

• aftur = back or again
• inn = in / inside, with a sense of movement inward

Together, aftur inn means something like:

• back inside
• back in

So it is not redundant. Aftur tells you there is a return, and inn tells you the direction of movement.

Because inn is used for movement, while inni is used for location.

Compare:

• fara inn = to go in
• vera inni = to be inside

In your sentence, she is moving, so Icelandic uses inn:

• fór aftur inn = went back in

If the sentence were describing where she was, not where she went, you would expect inni instead.

Gerði is the past tense of gera, which means to do or to make.

Here it is 3rd person singular past:

• gera = to do / make
• gerði = did / made

So:

• gerði litla innborgun = made a small deposit

This is a very common verb in Icelandic, so it is worth learning early.

Because lítil is the nominative form, but here the phrase is the direct object of gerði, so it must be in the accusative.

• lítil innborgun = a small deposit (subject form / nominative)
• litla innborgun = a small deposit (object form / accusative)

More specifically:

• innborgun is feminine singular
• the adjective must agree with it
• the accusative feminine singular form of lítill / lítil / lítið here is litla

So the sentence needs litla, not lítil.

Because some Icelandic nouns have the same form in the nominative and accusative singular.

That is what happens here:

• innborgun = nominative singular
• innborgun = accusative singular as well

So even though the noun is the direct object, its form does not visibly change. The case is shown mainly by:

• the sentence structure
• the verb gerði
• the adjective form litla

This is very common in Icelandic, so learners often need to rely on the adjective or article to see the case clearly.

Because the subject is the same in both parts of the sentence, and Icelandic often leaves the repeated subject out in this kind of coordination.

So:

• fór hún aftur inn og gerði litla innborgun

means:

• she went back in and made a small deposit

The hún is understood for both verbs.

You could say og hún gerði..., but that would usually sound more explicit or emphatic than necessary.

Yes, it is a natural and understandable way to express make a deposit.

That said, Icelandic also often uses other banking expressions depending on context, such as forms of leggja inn. So learners may see more than one way to talk about depositing money.

In this sentence, gerði litla innborgun is a straightforward way to say that she made a small deposit.