You used 'the' correctly in each sentence. Your sentences are put together correctly, so good job. The way Keith corrected it sounds more natural and is the way a natural speaker would probably word it. However, your use of the word in those sentences is not incorrect.

The use of 'the' is correct for all except #8, it does not sound correct. If you want to use 'the' in the sentence, it should be, "He is a doctor but the doctor is not kind." 'Are' should be changed to 'is'. On a side note, for some of these if you wanted, you could drop the 'the' altogether and the sentence would still flow well grammar wise.

NO, these are all wrong, sorry! - and they are all the same! You don't use 'the' if you introduce something then talk about it. It should be like this: 1. This is a letter. It's written in Spanish. 2. It is a box. It's red. I'll open it and.. 8 He is a doctor, but he's not kind. You use 'the' later, when you reference something from before: The box I received is red/ The doctor I went to was rude. Or, if there are 2 or more: I got 2 boxes; the big one is from.. and the small one is from.. :)

Yep, actually a lot of Asian students have no idea how to use 'a' and 'the' you see. That's not in terms of where to put them in a sentence or grammatically but what their function is. They tell me all the time that they've been taught that 'a' should be used first, and then 'the', which leads to the kind of sentences Tâm has made. I immediately recognised that the two sentences in each example are to be taken as one following the other, as she's querying what she's probably been taught. :)

I see what you mean Keith. My reasoning behind answering yes she is correct for where she is applying the "the" to a sentence is because she specifically said she was learning about that word. Therefore, the use of 'the' in these sentences is correct. If she were trying to create a natural sounding sentence, I would omit 'the' from a lot of those sentences.