На рынке мы купили сладкую дыню и два спелых персика к ужину.

На рынке means at the market or in the market in the sense of being there as a place/activity.

Here на is used with the prepositional case to show location, and рынок becomes рынке.

• рынок = market
• на рынке = at the market

Russian often uses на with places that English might express with at:

• на работе = at work
• на почте = at the post office
• на рынке = at the market

So this is not a word-for-word on the market meaning. It is just the normal Russian expression.

Мы means we, so the verb has to match a plural subject.

Купили is the past tense plural form of купить.

• купить = to buy (perfective)
• купили = bought / did buy

In the past tense, Russian verbs agree with the subject in gender/number:

• я купил / купила = I bought
• он купил = he bought
• она купила = she bought
• мы купили = we bought

So мы купили simply means we bought.

Russian uses aspect to show how an action is viewed.

• купить / купили = perfective: the action is seen as completed
• покупать / покупали = imperfective: the action is ongoing, repeated, or just described as a process

In this sentence, the speaker is talking about a completed result: they went to the market and ended up buying those things. So купили is the natural choice.

Compare:

• На рынке мы купили сладкую дыню... = At the market we bought a sweet melon...
• На рынке мы покупали фрукты = At the market we were buying fruit / used to buy fruit

Because дыню is the direct object of купили (we bought what?), it goes into the accusative case.

The noun дыня is feminine singular, so in the accusative singular it becomes:

• дыня → дыню

The adjective must agree with the noun in gender, number, and case, so:

• сладкая → сладкую

So:

• сладкая дыня = a sweet melon
• купили сладкую дыню = bought a sweet melon

This is a very common Russian number pattern.

After два / три / четыре with nouns like this:

• the noun usually takes the genitive singular
• the adjective usually takes the genitive plural

So:

• персик → персика
• спелый → спелых

That gives:

• два спелых персика = two ripe peaches

This pattern often feels strange to English speakers because English just keeps the plural:

• two ripe peaches

But Russian uses a special structure after 2, 3, 4.

Because after два, Russian normally uses the genitive singular form of the noun.

So even though the meaning is plural (two peaches), the noun itself appears in a form that is historically and grammatically singular:

• один персик = one peach
• два персика = two peaches
• пять персиков = five peaches

This is one of the number rules you simply have to get used to in Russian.

As a whole, it is functioning as a direct object of купили, so it is in the accusative.

However, number expressions in Russian are special. With два, the phrase looks like this:

• два = nominative/accusative form of the numeral
• спелых = genitive plural adjective
• персика = genitive singular noun

So even though the whole phrase is the object of the verb, the words inside the phrase follow the normal number construction used after 2.

Here к means something like for, by, or for the time of dinner.

• ужин = dinner
• к ужину = for dinner / for the evening meal / by dinnertime

The preposition к takes the dative case, so:

• ужин → ужину

In this sentence, к ужину suggests that the melon and peaches were bought for dinner or to have with dinner.

Yes, sometimes на ужин is possible, but the nuance is a little different.

• к ужину often suggests for dinner / by dinner time
• на ужин often means for dinner as a meal occasion

In many contexts they can be close in meaning, but к ужину sounds very natural here for food bought with dinner in mind.

Russian has no articles, so there is no direct equivalent of a, an, or the.

So:

• дыню can mean a melon or the melon
• персика can mean peaches in context

English has to choose:

• we bought a sweet melon and two ripe peaches
• we bought the sweet melon and the two ripe peaches

Russian leaves that to context.

Yes, Russian word order is fairly flexible because the case endings show each word’s role.

This sentence is perfectly natural:

• На рынке мы купили сладкую дыню и два спелых персика к ужину.

But other orders are also possible, with different emphasis:

• Мы купили на рынке сладкую дыню и два спелых персика к ужину.
• Сладкую дыню и два спелых персика мы купили на рынке.

The original version puts На рынке first, which gives a natural setting or context: At the market, we bought...

Here и is just the normal conjunction and:

• сладкую дыню и два spелых персика = a sweet melon and two ripe peaches

Nothing unusual is happening with и in this sentence. It links two direct objects of купили.

Because the two noun phrases are built differently.

1. сладкую дыню

   • one noun
   • feminine singular accusative
   • adjective agrees directly with the noun

2. два спелых персика

   • a numeral phrase with два
   • after два, Russian uses a special pattern
   • adjective becomes genitive plural
   • noun becomes genitive singular

So the forms are different not because one adjective behaves differently on its own, but because the whole grammar of the phrase changes after два.