Я купил груши и бананы на рынке, а потом ещё взял кефир.

Because the sentence describes completed, one-time actions in a sequence:

• купил = bought (completed)
• взял = took / picked up / got (completed)

These are perfective past-tense forms. Russian often uses the perfective aspect when telling what happened next in a finished chain of events.

If you used покупал or брал, that would be imperfective, which usually suggests:

• process,
• repetition,
• background action,
• or an action without focus on completion.

So this sentence sounds like a short finished story: first I bought fruit, then I picked up kefir.

That is the normal marker of the past tense in Russian.

In the singular past tense, Russian also shows gender:

• купил, взял = masculine speaker
• купила, взяла = feminine speaker
• купило, взяло = neuter subject
• купили, взяли = plural

So Я купил... tells you the speaker is male. If the speaker were female, it would be Я купила груши и бананы...

They are the direct objects of the verb купил, so they are in the accusative case.

Here is the important point:

• for inanimate plural nouns, the accusative plural is the same as the nominative plural

So:

• груши = nominative plural / accusative plural
• бананы = nominative plural / accusative plural

Compare singular:

• груша → грушу in the accusative singular
• банан → банан in the accusative singular, because masculine inanimate singular often looks like the nominative

So Я купил груши и бананы means I bought pears and bananas.

Because груш is the genitive plural, not the accusative plural.

You often see груш after numbers or quantity words, for example:

• много груш = many pears
• пять груш = five pears

But after купил here, you need the direct object, so the form is груши.

Because на рынке means at the market — a location.

Russian uses different cases depending on whether you mean:

• location: на рынке = at the market
• motion toward a place: на рынок = to the market

So:

• Я купил груши на рынке = I bought pears at the market
• Я пошёл на рынок = I went to the market

Here the speaker is already there, so на рынке is correct.

А потом means and then / and after that.

The conjunction а often shows a transition, slight contrast, or a move to the next part of the story. It is very natural in Russian storytelling.

So this sentence has the feel of:

• I bought pears and bananas at the market, and then I also picked up kefir.

You could sometimes use и потом, but а потом often sounds more natural when moving from one action to the next with a slight shift in focus.

Here ещё means something like:

• also
• in addition
• one more thing
• besides that

So а потом ещё взял кефир means:

• and then I also picked up kefir
• and then I got kefir as well

Be careful: ещё can mean different things in other contexts, such as still or yet. But in this sentence it clearly means in addition.

Both are possible, but the nuance is a little different.

• купил кефир = explicitly bought kefir
• взял кефир = took / picked up / got kefir

In shopping contexts, взять is very common and natural. It often sounds a bit more conversational, as if you are listing what you grabbed while shopping.

So the sentence suggests:

• first the speaker bought pears and bananas,
• then he also picked up kefir.

Russian does not have articles like a, an, and the.

So кефир can mean:

• kefir
• some kefir
• the kefir

The exact meaning comes from context.

Also, кефир is normally treated as a mass noun, like milk. So English often says some kefir, while Russian can simply say кефир.

If you want to mention a container, Russian often uses:

• бутылку кефира = a bottle of kefir
• пакет кефира = a carton/package of kefir

In this sentence, я is natural and helpful.

Russian often drops subject pronouns when the subject is clear, but in the past tense the verb does not show person. It only shows gender and number:

• купил = bought, masculine singular
• but it does not itself say I or he

So without context, купил could mean:

• I bought (if a male speaker is talking)
• or he bought

That is why Я купил... is very normal in an isolated sentence.

In conversation, if the subject is already obvious, Russian can drop я:

• Купил груши и бананы, а потом ещё взял кефир.

Yes. Russian word order is flexible, and changing it changes the emphasis, not the basic meaning.

The original sentence is neutral and natural:

• Я купил груши и бананы на рынке, а потом ещё взял кефир.

Other possible orders:

• На рынке я купил груши и бананы, а потом ещё взял кефир.
  Emphasizes at the market.

• Потом я ещё взял кефир.
  Emphasizes then.

• Кефир я потом ещё взял.
  Emphasizes kefir.

So yes, the words can move, but the original order is a good standard one for a learner.

Because а is joining two parts of the sentence, and Russian normally uses a comma before а in this kind of structure.

The two parts are:

1. Я купил груши и бананы на рынке
2. а потом ещё взял кефир

Even though the subject is logically the same person, Russian punctuation still normally puts a comma before а here.

So the comma is standard and expected.