Learn Polish: U mojego prawnika prowadzą zupełnie inną działalność. - At my lawyer's office, they run a completely different business.

For abstract, idiomatic expressions like running a business (prowadzić działalność), keeping a diary, or leading a meeting, Polish almost always locks into the unidirectional verb prowadzić. The multidirectional prowadzać is rarely used in abstract ways and is mostly reserved for literal, repeated physical leading, like walking a dog.

How do we know działalność is in the accusative case if it doesn't end in -ę?

Działalność is a feminine noun ending in a consonant. For this specific group of nouns, the accusative form is exactly the same as the nominative. The big clue that it is the direct object here (accusative) is the adjectives preceding it: zupełnie inną take the standard feminine accusative -ą ending.

Why does the sentence say u mojego prawnika instead of explicitly mentioning an office?

Just like in English where we say 'at the doctor's' or 'at my lawyer's', Polish uses the preposition u followed by the genitive case of a person to mean 'at their place' or 'at their office'. It sounds much more natural here than literally translating 'in the office of my lawyer'.

Since the sentence has no pronoun like oni, who is the subject of prowadzą?

The subject is an implied 'they', but it acts as an impersonal construction. Polish frequently uses the third-person plural without a pronoun to refer to 'people in general' or 'the staff there', similar to the English phrase 'they do things differently over there'.