Learn Italian: I miei commessi sono occupati. - My shop assistants are busy.

In Italian, possessive adjectives almost always need a definite article before them. The main exception is when you are talking about singular family members (like mio padre). Since commessi (shop assistants) aren't family, we must use the article i.

Does commessi refer only to male shop assistants?

Not necessarily. While a purely female group of shop assistants would be le commesse, Italian grammar dictates that a mixed group of men and women defaults to the masculine plural i commessi.

Could I use impegnati instead of occupati here to say they are busy?

Yes, impegnati is a great alternative when talking about people being busy with tasks or work. Occupati is also perfectly natural for people, and it is the word you must use for a physical space being occupied or taken, like a restroom or a seat.

How would I use an indefinite adjective like qualsiasi to say 'Any shop assistant is busy'?

If you wanted to say 'Any shop assistant is busy' instead of 'My shop assistants', you would drop the possessive and change the sentence to singular. You would say Qualsiasi commesso è occupato, because indefinite adjectives like qualsiasi and qualunque must be followed by a singular noun.