Mamy już kupione mandarynki i borówki na weekend.

Both are possible, but they focus on slightly different things.

• Kupiliśmy już mandarynki i borówki na weekend = We already bought tangerines and blueberries for the weekend.
• Mamy już kupione mandarynki i borówki na weekend = We already have the tangerines and blueberries bought / taken care of for the weekend.

So mamy + kupione emphasizes the resulting state: the shopping is done, the matter is settled. It often sounds a bit like we’ve already got that sorted.

Kupione is a passive participle formed from kupić (to buy).

It is not the normal past tense.
The normal past tense would be:

• kupiłem / kupiłam = I bought
• kupiliśmy = we bought

In mamy już kupione, the participle works with mamy to create a resultative meaning: we have it bought, meaning it is already bought from our point of view.

Because it agrees with mandarynki i borówki.

Those nouns together are:

• plural
• non-masculine-personal

In Polish, adjectives and participles must agree with the nouns they describe. For a plural non-masculine-personal noun phrase, the typical ending is -e.

So:

• kupione mandarynki
• kupione borówki
• kupione mandarynki i borówki

If the noun phrase were masculine-personal, the form would be different.

They are the direct object of mamy in this construction, so they are in the accusative plural.

For these particular nouns, the accusative plural looks the same as the nominative plural:

• mandarynki
• borówki

So even though the case is accusative, there is no visible change here.

Literally, mamy means we have.

But in this sentence, it does not just mean simple possession in the ordinary sense. It is part of the pattern:

• mieć + participle + object

This often means to have something done / completed / arranged.

So mamy już kupione... is not just we possess...
It is more like we already have ... bought or we already have ... taken care of.

Już means already.

In this sentence it marks that the buying has been completed before now. Polish word order is flexible, so już can move around a bit depending on emphasis:

• Mamy już kupione mandarynki i borówki na weekend.
• Już mamy kupione mandarynki i borówki na weekend.

Both are natural.
The version with już after the verb is very neutral.

Na weekend means for the weekend.

It suggests purpose or intended use: the fruit is bought for the coming weekend.

This is different from:

• w weekend = during the weekend

So:

• kupione na weekend = bought for the weekend
• kupione w weekend = bought during the weekend

Also, na requires the accusative here. With weekend, the accusative singular looks the same as the basic form, so you still see weekend.

It can often be translated that way, but it is not exactly the same grammatical tense.

Polish does not have a direct equivalent of the English present perfect. Instead, Polish uses other ways to express that idea, depending on what is being emphasized.

Here:

• Kupiliśmy już... can often translate as We’ve already bought...
• Mamy już kupione... can also translate that way, but it stresses the current result more strongly

So the English translation may be similar, but the Polish structure is doing something a bit different.

The word order is not fixed. Polish allows quite a lot of flexibility.

For example, these are all possible:

• Mamy już kupione mandarynki i borówki na weekend.
• Już mamy kupione mandarynki i borówki na weekend.
• Mandarynki i borówki mamy już kupione na weekend.

The differences are mostly about emphasis, not basic meaning.

The original version sounds natural and neutral.
If you move mandarynki i borówki to the front, you highlight those items more strongly.

Usually it suggests that we are responsible for the result: the fruit has been bought and this task is done from our point of view.

It often implies that we bought them, but it does not absolutely have to. Depending on context, it could also mean that the buying was arranged for us or done on our behalf.

The main point is the completed state:

• the mandarins and blueberries are already bought
• that part of the weekend prep is done