Wir kaufen im Einkaufszentrum ein.

Because the verb here is einkaufen, which is a separable verb.

• The full infinitive is einkaufen = to shop
• It is made of:
  • ein- = the separable prefix
  • kaufen = the main verb part

In a normal main clause, German often splits separable verbs:

• Wir kaufen ... ein.

So the conjugated part kaufen goes in the usual verb position, and the prefix ein moves to the end.

Compare:

• Ich kaufe ein. = I shop / I am shopping.
• Wir kaufen im Einkaufszentrum ein.

They are related, but they are not exactly the same.

• kaufen usually means to buy
• einkaufen usually means to shop or to do some shopping

So:

• Wir kaufen ein. = We are shopping.
• Wir kaufen Brot. = We are buying bread.

In many contexts, einkaufen focuses more on the activity of shopping, not just the act of purchasing one specific thing.

im is a contraction of in dem:

• in dem → im

So:

• im Einkaufszentrum = in the shopping center

You need an article here because Einkaufszentrum is a noun, and in this sentence it refers to a specific kind of place: the shopping center.

German often uses these contractions:

• im = in dem
• am = an dem
• zum = zu dem
• zur = zu der

Because in is a two-way preposition in German. That means it can take either:

• accusative for movement toward a destination
• dative for location

Here, the sentence describes where the shopping happens, not movement into the place:

• Wir kaufen im Einkaufszentrum ein. = We shop in the shopping center.

So it uses dative.

Compare:

• Wir gehen in das Einkaufszentrum. = We go into the shopping center.
  
  • movement → accusative
• Wir sind im Einkaufszentrum. = We are in the shopping center.
  
  • location → dative

Yes. In dem Einkaufszentrum is grammatically correct.

But in everyday German, im is much more natural and common.

So both mean the same thing:

• Wir kaufen im Einkaufszentrum ein.
• Wir kaufen in dem Einkaufszentrum ein.

Usually, learners should prefer im unless there is some special emphasis.

Because German very often forms compound nouns by joining words together.

Here:

• Einkauf = shopping / purchase
• Zentrum = center

So:

• Einkaufszentrum = shopping center

This is completely normal in German. English often writes these as separate words, but German usually joins them into one noun.

Also notice that all nouns in German are capitalized, so Einkaufszentrum starts with a capital letter.

Yes, it is in the present tense:

• wir kaufen ... ein

German present tense can cover several English ideas depending on context:

• We shop in the shopping center.
• We are shopping in the shopping center.
• We do our shopping in the shopping center.

German does not need a separate form like English are shopping in order to express an action happening now.

The basic structure is:

• Wir = subject
• kaufen = conjugated verb
• im Einkaufszentrum = location
• ein = separable prefix at the end

So the pattern is:

Subject + conjugated verb + other information + separable prefix

This is very common in German main clauses.

You can also move other elements to the front for emphasis, but the conjugated verb still stays in second position:

• Im Einkaufszentrum kaufen wir ein.

That still means the same thing, but now the location is emphasized.

In a subordinate clause, the separable verb usually becomes unsplit again and goes to the end as one unit.

Main clause:

• Wir kaufen im Einkaufszentrum ein.

Subordinate clause:

• ..., weil wir im Einkaufszentrum einkaufen.
  = ..., because we shop in the shopping center.

So:

• main clause: kaufen ... ein
• subordinate clause: einkaufen

This is a very important pattern with separable verbs.

The clue is the separable prefix ein.

• wir kaufen by itself could mean we buy
• wir kaufen ... ein is from einkaufen, which means to shop

So the little word at the end changes the meaning of the verb.

That is why it is important not to ignore sentence-final particles like ein, auf, mit, an, and so on. With separable verbs, that final piece is part of the verb’s meaning.