Learn Italian: Perché inizi il progetto in ritardo? - Why do you start the project late?

It actually means both! In Italian, perché is used to ask 'why' (as it does here at the beginning of the sentence) and it is also used to answer 'because'.

Where is the word for 'do' in this question?

Italian doesn't use extra helping words like 'do' or 'does' to ask questions. You just put the question word (perché) right before the verb (inizi).

How do we know this means 'do you start' when the word for 'you' isn't there?

The 'you' is built right into the verb. Inizi is the informal 'you' (tu) form of the verb iniziare (to start), which we can tell by its -i ending. Italian usually drops words like 'I' or 'you' because the verb ending already tells us who is doing the action.

Why do we say in ritardo instead of just a single word for 'late'?

In ritardo literally translates to 'in delay.' This is the standard phrase Italians use to describe an action, person, or thing running behind schedule.