Το σερβίτσιο είναι χειροποίητο, μόνο που έχει ραγισμένο κεραμικό.

Because σερβίτσιο is a neuter singular noun in Greek, so anything that agrees with it also has to be neuter singular.

• το σερβίτσιο = the set / the dinner service / the tableware set
• χειροποίητο = handmade

So Greek is matching the adjective to the noun:

• το σερβίτσιο
• είναι χειροποίητο

If the noun were feminine or masculine, the adjective would change too.

For example:

• η κούπα είναι χειροποίητη = the mug is handmade
• ο δίσκος είναι χειροποίητος = the tray is handmade

Σερβίτσιο usually means a set of dishes / service / tableware set, not just one plate or one cup.

Depending on context, it can mean:

• a dinner set
• a coffee set
• a tea set
• a matching set of ceramic items

So it is often a collective noun: grammatically singular, but referring to a group of matching pieces.

Yes, it is very common. Χειροποίητο means handmade or handcrafted.

It comes from:

• χέρι = hand
• a form related to make/do

So literally it is something like made by hand.

You will often see it in shops, markets, and product descriptions:

• χειροποίητο κόσμημα = handmade jewelry
• χειροποίητο σαπούνι = handmade soap
• χειροποίητα κεραμικά = handmade ceramics

Here μόνο που means something like:

• except that
• only that
• but

It introduces a limitation or a small negative point after something positive.

So the structure is basically:

• It is handmade, only/except that...
• It is handmade, but...

This is very natural in Greek.

Examples:

• Θα ερχόμουν, μόνο που δουλεύω. = I would come, except that I’m working.
• Το φόρεμα είναι ωραίο, μόνο που είναι ακριβό. = The dress is nice, but it’s expensive.

Έχει means it has, so the sentence is presenting the crack as a feature/problem that the set has.

Greek often uses έχει for defects:

• έχει γρατζουνιά = it has a scratch
• έχει λεκέ = it has a stain
• έχει ράγισμα = it has a crack

If you say είναι ραγισμένο, that means it is cracked. That is also possible, but it focuses more directly on the state of the object.

So the difference is roughly:

• έχει... = it has some damage / defect
• είναι ραγισμένο = it is cracked

Ραγισμένο is the neuter singular form of the participle/adjectival form from ραγίζω, which means to crack.

So:

• ραγισμένος = masculine
• ραγισμένη = feminine
• ραγισμένο = neuter

It functions like an adjective meaning:

• cracked
• split
• having a crack

Examples:

• ραγισμένο ποτήρι = a cracked glass
• ραγισμένη κούπα = a cracked mug
• ραγισμένο πιάτο = a cracked plate

It can be either, depending on context.

As an adjective:

• κεραμικό πιάτο = ceramic plate

As a noun:

• ένα κεραμικό = a ceramic item / a piece of pottery / a ceramic object

In your sentence, κεραμικό is being used like a noun, meaning something like ceramic piece or ceramic item.

That is why ραγισμένο agrees with it in neuter singular:

• ραγισμένο κεραμικό

It is understandable, but many native speakers would probably find it a bit awkward or incomplete, depending on the intended meaning.

Why? Because κεραμικό is somewhat broad. A listener may wonder:

• Do you mean one ceramic piece in the set?
• Do you mean the ceramic material is cracked?
• Do you mean the whole set has a cracked item?

More natural alternatives might be:

• μόνο που έχει ένα ραγισμένο κομμάτι = except that it has a cracked piece
• μόνο που ένα κεραμικό είναι ραγισμένο = except that one ceramic piece is cracked
• μόνο που έχει ράγισμα στο κεραμικό = except that it has a crack in the ceramic

So the original is understandable, but not the most idiomatic wording in every context.

Without the article, it sounds more indefinite:

• has a cracked ceramic piece / has cracked ceramic

If you added the article:

• έχει το ραγισμένο κεραμικό

that would sound like it has the cracked ceramic item, which usually only works if the speaker and listener already know exactly which item is being referred to.

Greek often leaves out the article in predicate-like or indefinite expressions after έχει.

Not always. A very literal translation is sometimes only that, but in natural English the best translation often changes depending on context:

• but
• except that
• only
• the only problem is that

In this sentence, English would probably prefer:

• The set is handmade, but it has a cracked ceramic piece. or
• The set is handmade, except that one ceramic piece is cracked.

So it is better to learn μόνο που by function, not by one fixed English translation.