Learn Arabic (Modern Standard): أخذ المفتاح رقم سبعة.

We aren't counting a quantity of keys here (which would use different grammar). Instead, we are just naming the digit 'seven'. When naming digits or using numbers as labels, Arabic uses the 'bare counting form.' For numbers 3 to 10, this default counting form has the feminine ending.

Where is the word for 'he' in this sentence?

It is built right into the verb. The word أخذ means 'he took' all by itself. In Arabic, you don't need to add the separate pronoun هو (he) unless you want to emphasize who did the taking.

Why do we need the word رقم here? Couldn't we just say المفتاح سبعة?

In English, we can sometimes just say 'Key seven', but in Arabic, it is much more natural to include the word رقم (number) when a number is used as an ID or label. So, you literally say 'the key, number seven'.

Why does المفتاح have the prefix for 'the' but رقم سبعة does not?

The word المفتاح is a specific object being taken, so it needs the definite article prefix to mean 'the key'. However, the phrase رقم سبعة (number seven) acts like a proper name or a fixed label for that key, so it doesn't need 'the'.