I have two questions concerning my sentence:
Is "duties" the correct word for my context (I'm talking about doing homework)? In case it is, does it mean moral obligations in this sentence?
Which word is better for my context (everything or anything)? Why?
If you do your duties first, you'll have more time to do everything / anything you want during the weekend.
No, we would not normally refer to homework as a "duty" (at least in American English). Usually we would just say "do your homework". If you want to include other activities, then you could call them "chores" (although chores are often considered separate from homework) or perhaps "obligations" (which sounds more formal and would require a different verb).
Either word ("everything" or "anything") would work, but their meanings are different. If the person wants to do three things during the weekend and can do all of them, then use "everything". If the person can do any of those things but not necessarily all three, then use "anything".
