كعكة الزفاف وخاتم الزواج على الطاولة.

Because this is a nominal sentence in Arabic. In the present tense, Arabic usually does not use a verb like is/are.

So:

• كعكة الزفاف وخاتم الزواج على الطاولة = The wedding cake and the wedding ring are on the table

The structure is basically:

• كعكة الزفاف وخاتم الزواج = the wedding cake and the wedding ring
• على الطاولة = on the table

Arabic simply puts them together, and the meaning are is understood.

If you wanted a past-tense version, then Arabic would normally use a verb, for example:

• كانت كعكة الزفاف وخاتم الزواج على الطاولة = The wedding cake and the wedding ring were on the table.

Because كعكة الزفاف is an iḍāfa (إضافة), often called a construct phrase.

In an iḍāfa:

• the first noun usually does not take الـ
• the whole phrase becomes definite or indefinite based on the second noun

So:

• كعكة زفاف = a wedding cake
• كعكة الزفاف = the wedding cake

The same thing happens with:

• خاتم الزواج = the wedding ring

Even though كعكة and خاتم do not have الـ, the whole phrases are definite because الزفاف and الزواج are definite.

It is an iḍāfa phrase made of two nouns:

• كعكة = cake
• الزفاف = the wedding

Literally, it is something like the cake of the wedding, but natural English says the wedding cake.

This is a very common Arabic pattern for noun combinations:

• باب البيت = the door of the house / the house door
• مدير المدرسة = the principal of the school / the school principal
• خاتم الزواج = the wedding ring

So كعكة الزفاف is not an adjective phrase. It is a noun + noun structure.

They are related, but not exactly identical.

• الزفاف usually refers more specifically to the wedding ceremony or wedding event
• الزواج usually refers more broadly to marriage or the state/institution of marriage

So:

• كعكة الزفاف = wedding cake
  This fits well because a wedding cake is associated with the wedding event.

• خاتم الزواج = wedding ring / marriage ring
  This fits because the ring is associated with marriage itself.

In real usage, there can be overlap, but this pairing sounds natural.

Because و is a clitic in Arabic, meaning it is written attached to the following word.

So:

• و = and
• خاتم = ring
• together: وخاتم = and a ring / and the ring

This is normal Arabic spelling. Many short particles attach directly to the next word, including:

• و = and
• ب = with/by
• ل = to/for
• ك = like/as

Yes, Arabic word order is fairly flexible.

In this sentence:

• كعكة الزفاف وخاتم الزواج = topic / subject-like part
• على الطاولة = predicate-like part

So the sentence means:

• The wedding cake and the wedding ring are on the table

This order is very natural.

Arabic can sometimes move parts around for emphasis, but the version you have is straightforward and standard.

Because it means the table, not just a table.

• طاولة = a table
• الطاولة = the table

So:

• على طاولة = on a table
• على الطاولة = on the table

The definite article الـ works much like the in English.

A fully vocalized version would normally be:

كَعْكَةُ الزِّفَافِ وَخَاتَمُ الزَّوَاجِ عَلَى الطَّاوِلَةِ

Here is why:

• كعكةُ — nominative, because it is part of the subject/topic of the nominal sentence
• الزفافِ — genitive, because it is the second term of an iḍāfa
• خاتمُ — nominative, coordinated with كعكةُ
• الزواجِ — genitive, because it is also the second term of an iḍāfa
• الطاولةِ — genitive, because it comes after the preposition على

In everyday writing, these short vowels are usually omitted.

Because كعكة ends in ة (tāʾ marbūṭa).

When a word with ة is said by itself, it is usually pronounced like -a(h):

• كعكة ≈ kaʿka

But when it is followed by another word in an iḍāfa, the ة is pronounced as t:

• كعكة الزفاف ≈ kaʿkat az-zifāf

So the t sound appears because the word is connected grammatically to the next noun.

Because ز is a sun letter.

When الـ comes before a sun letter, the l sound is assimilated to the next consonant. So:

• الزفاف is pronounced az-zifāf
• الزواج is pronounced az-zawāj
• الطاولة is pronounced aṭ-ṭāwila

This affects pronunciation, but the spelling usually stays the same.

Because in an iḍāfa, the first noun does not take tanwīn.

Compare:

• كعكةٌ = a cake
• خاتمٌ = a ring

But in an iḍāfa:

• كعكةُ الزفافِ
• خاتمُ الزواجِ

The first noun loses tanwīn because it is grammatically linked to the second noun.

Yes. The phrase على الطاولة applies to both:

• كعكة الزفاف
• خاتم الزواج

So the meaning is:

• The wedding cake and the wedding ring are on the table

Arabic often places the location phrase once at the end, just as English can do.

A very literal translation would be:

• Cake of the wedding and ring of the marriage on the table.

But that is not natural English.

A good natural translation is:

• The wedding cake and the wedding ring are on the table.

This is a good example of how Arabic often uses noun + noun structures where English may use:

• a noun modifier (wedding cake)
• or of (ring of marriage, though English would usually say wedding ring)