All three of these are incorrect. After correcting them, they will have different meanings. First: "finished *the* lunch" means that you are doing something to the lunch. Maybe you're cooking it, maybe you're arranging it on a plate, maybe you're putting it in a backpack - what you're absolutely not doing is eating it. If you want to talk about eating, you use the phrase "finished lunch." Second: "Have you finished lunch already?" - This would be said to someone who is eating very quickly or who has eaten earlier than expected. If your schedule was for lunch to go from 12 to 1, and at 12:05 the person's lunch was eaten, you could ask "Have you finished lunch already?" "Have you finished lunch yet?" - This would be said if you did not know whether or not the person had eaten. "Haven't you finished lunch yet?" - This would be said to someone who is eating very slowly or who is eating later than expected. Again, if you planned on lunch between 12 and 1, and it's 1:30 and that person is still eating, you could ask "Haven't you finished lunch yet?"

This looks like another stupid test devised by a Chinese teacher. I have been dealing with this idiocy for fifteen years and it really annoys me. Your teachers are wasting your time with this rubbish, instead of teaching you how to use English. "I don't know how to use 'yet'." "How do you use 'yet'?" These are both correct. "how to use 'yet'" is Chinglish. Not only is it ungrammatical, you forgot that sentences start with capital letters and end with some kind of punctuation. If you're asking a question, use a question mark. If you're making a statement, use a full stop. You know this already, right? But you don't do it automatically YET, like native speakers do. All the international tests require you to write proper sentences. If you want to learn English to international standards, you need to start paying attention to the rules you know, today, right now and every moment from now on, before worrying about this stuff. Please tell your teacher that the single most commonly-used word in the English language is "the". And you can't use it correctly YET. This means that almost everything you write contains errors. You CAN do it right, you're not stupid, but your teachers need to focus on the basics. It's good that you're using this site to look for help. You obviously care a lot and are a diligent student. It just makes me sad that you are learning the wrong things! :(

Don't use "the". It's "lunch" or "your lunch". Apart from that, you could use any of those sentences in the right situation.

"Have you finished your lunch already?" is correct. "Have you finished your lunch yet?" is also correct. "Haven't you finished your lunch yet?" is also correct. Each sentence would be correct if you insert the word "your" in the place of "the".