Το ξυράφι είναι πάνω στο περβάζι, δίπλα στην πετσέτα.

Το is the definite article for a singular neuter noun in the nominative case.

Here, το ξυράφι means the razor.
Greek usually uses the article more regularly than English, so when you are talking about a specific object, the article is normally included.

Ξυράφι is neuter.

That is why it takes the article το:

• το ξυράφι = the razor

A useful pattern: many Greek nouns ending in -ι are neuter, though not all nouns can be guessed from the ending alone.

Είναι is the present-tense form of είμαι, meaning is / am / are.

In this sentence, it is simply linking the subject to its location:

• Το ξυράφι είναι... = The razor is...

Greek commonly uses είναι for location, just as English uses is.
You might also hear βρίσκεται in some contexts, which is a bit more formal or explicit, but είναι is completely normal here.

Πάνω adds the idea of on top of or on the surface of.

So:

• στο περβάζι can mean at/on the windowsill, depending on context
• πάνω στο περβάζι makes it clearer that the razor is resting on top of the sill

English often uses on, and Greek often expresses that more explicitly with πάνω σε.

Στο is a contraction of:

• σε
  • το → στο

So στο περβάζι literally comes from σε το περβάζι, but Greek contracts this automatically.

Depending on context, σε can mean:

• in
• on
• at
• to

So πάνω στο περβάζι is literally on the windowsill.

It is in the accusative case after σε, but with this noun, the form happens to stay the same.

For many neuter nouns in Greek, the nominative and accusative singular look identical:

• nominative: το περβάζι
• accusative: το περβάζι

So even though the grammar changes, the noun itself does not visibly change here.

Yes, usually δίπλα is followed by σε or sometimes από.

Here you have:

• δίπλα στην πετσέτα

This contains σε, because:

• σε
  • την → στην

So this is basically:

• δίπλα σε την πετσέτα → δίπλα στην πετσέτα

That is the normal Greek way to say next to the towel.

Because after the preposition σε, Greek uses the accusative case, not the nominative.

So:

• nominative: η πετσέτα = the towel
• accusative: την πετσέτα

And with contraction:

• σε την πετσέτα → στην πετσέτα

The noun πετσέτα itself stays the same in form here, but the article changes from η to την.

Because many feminine nouns ending in -α have the same form in the nominative and accusative singular.

So:

• η πετσέτα = nominative
• την πετσέτα = accusative

The difference shows up mainly in the article, not the noun ending.

This is a very common question.

• πάνω σε = on, on top of, with contact
• πάνω από = above / over, not necessarily touching

So in this sentence:

• πάνω στο περβάζι means the razor is on the windowsill

If you said πάνω από το περβάζι, it would sound like the razor is above the windowsill, not resting on it.

The comma separates two location phrases:

• πάνω στο περβάζι
• δίπλα στην πετσέτα

It helps show a small pause and adds the second piece of location information.
In informal writing, people might sometimes omit the comma, but with the comma the sentence feels nicely structured and clear.

Because the final -ν is normally kept before certain sounds, including π.

Since πετσέτα starts with π, the standard form here is:

• στην πετσέτα

You may sometimes see variation in less formal writing in other contexts, but here στην is the expected standard form.

Yes. Greek word order is more flexible than English word order because articles and case forms give extra grammatical information.

The original sentence is a very natural, neutral way to say it:

• Το ξυράφι είναι πάνω στο περβάζι, δίπλα στην πετσέτα.

But Greek could also move things around for emphasis, for example:

• Πάνω στο περβάζι είναι το ξυράφι, δίπλα στην πετσέτα.

That sounds more marked or emphatic. For a learner, the original order is the safest and most natural one to use.

A rough guide is:

• Το ξυράφι είναι πάνω στο περβάζι, δίπλα στην πετσέτα.
• to ksee-RA-fee EE-ne PA-no sto per-VA-zee, THEE-pla steen pet-SE-ta

A few helpful points:

• ξ sounds like ks
• δ sounds like the th in this
• the stress mark shows which syllable is stressed:
  • ξυράφι
  • είναι
  • πάνω
  • περβάζι
  • δίπλα
  • πετσέτα

That stress is important in Greek, so it is worth paying attention to it early.