Μετά την ανακαίνιση της κουζίνας χρειάζεται ακόμα μια μικρή επισκευή στη βρύση.

In Modern Greek, μετά meaning after normally takes the accusative case. So την ανακαίνιση is accusative singular: μετά την ανακαίνιση = after the renovation.

You may also hear μετά από την ανακαίνιση, which means the same thing.

Because Greek uses the genitive here to mean of the kitchen.

So:

• η ανακαίνιση = the renovation
• της κουζίνας = of the kitchen

Together, η ανακαίνιση της κουζίνας means the renovation of the kitchen. This is a very common Greek pattern where English would often use of.

Χρειάζεται is the 3rd person singular present form of χρειάζομαι.

Depending on context, it can mean:

• he/she/it needs
• or more loosely is needed

That is why this form can sound slightly flexible in translation.

Greek often omits the subject pronoun when it is understood from context. English usually cannot do that, so English may need to add it or rephrase the sentence.

So Greek can say simply χρειάζεται..., while English may say:

• it still needs...
• or ...is still needed

This is a very normal feature of Greek.

From the form alone, you cannot tell.

In the feminine singular, these forms are the same in nominative and accusative:

• μια
• μικρή
• επισκευή

So μια μικρή επισκευή could be understood from context either as the thing that is needed or as the noun phrase involved in an impersonal-style expression. This is one reason the sentence can sound natural in English both as it still needs a small repair and a small repair is still needed.

Μια is the normal everyday spelling of the indefinite article/number a, one when it is not specially stressed.

The spelling μία also exists and may be used:

• for emphasis
• for clarity
• in slightly more careful or formal writing

But μια is extremely common and completely standard.

Here ακόμα means still.

Yes, ακόμα and ακόμη are basically interchangeable in Modern Greek. Some speakers feel that ακόμη is a bit more formal or written, but both are common.

In other contexts, ακόμα/ακόμη can also mean even, so the exact meaning depends on the sentence.

Στη is the contracted form of σε τη.

So:

• σε
  • τη βρύση → στη βρύση

After σε, Greek uses the accusative. Here that means τη βρύση, but after contraction you see στη βρύση.

In English, σε can correspond to in, on, at, to, depending on context. Here στη βρύση means something like on the faucet/tap or to the faucet/tap.

Greek sometimes keeps or drops the final -ν in forms like στη(ν) depending on the sound that follows.

Since βρύση starts with β, the usual form here is στη βρύση.

So this is mainly a spelling/pronunciation issue, not a difference in meaning.

It can mean both.

• In British English, tap is the more natural translation.
• In American English, faucet is the more natural translation.

In other contexts, βρύση can also refer to a water spout or fountain, but in a kitchen sentence it clearly means the kitchen tap/faucet.

They are related, but not the same.

• ανακαίνιση = renovation, remodeling, a larger improvement project
• επισκευή = repair, fixing a specific problem

So the sentence contrasts a big job with a small remaining fix: after the renovation, there is still one little repair left.

Yes. Greek word order is more flexible than English because grammatical relationships are often shown by endings and verb forms rather than position alone.

For example, you could also hear things like:

• Ακόμα χρειάζεται μια μικρή επισκευή στη βρύση.
• Μετά την ανακαίνιση της κουζίνας, χρειάζεται μια μικρή επισκευή ακόμα στη βρύση.

These versions are similar in meaning, but the emphasis shifts slightly depending on where words like ακόμα are placed.