Learn Finnish: Laadin luonnoksen loppuviikoksi. - I will draw up the draft by the end of the week.

In Finnish, the translative case (-ksi) is often used to indicate a deadline. Here, loppuviikoksi means the draft will be finished by the end of the week.

Can the -ksi ending also express how long something lasts? How do we know it is a deadline here?

Yes, the translative can also express an intended duration, like packing clothes "for the weekend". You can tell it means a deadline here because laatia (to draw up) is an action you complete, rather than a continuous state.

Why is the object luonnoksen in the accusative case that looks like the genitive?

It is a total object. Using the -n ending shows that the action will be fully completed: you will finish the entire draft. This also helps give the sentence its future meaning ("I will draw up"), since Finnish relies on the present tense and a total object to express future completion.

How does the dictionary word luonnos (draft) become luonnoksen?

For many Finnish words ending in -s (like luonnos, keskus, or rakennus), the stem changes the -s to -kse- before adding case endings. So the stem of luonnos is luonnokse-, to which we add the -n.