To address your question about what is "unnatural", it is often in the ear of the listener, and sometimes there is no other justification but for an educated native speaker to say "this sounds right to me and that does not". Personally, I hate to resort to that argument. It's like when a child asks her mother why she has to do something unpleasant and the mother answers "Because I said so!". So let me try to sort this out.
I was doing some questions about "used to" when i saw this question which puzzled me.
The meaning of the phrase "doing some questions" is unclear to me as such, so it sounds unnatural to me. My esteemed colleague Gustavo, who is brilliant in his analysis of English grammar even though it is not his first language, has provided the clue to what you might mean to say, that you are actually trying to address exercises in your ESL textbook. If that's true, just tell us. It makes things easier for us. Help us help you.
Your example (1) is a rare construct where I live, but it's easy to understand. The phrase "want to" can substitute for the single word "would". The fact that it is unusual does not make it incorrect, even though it might sound "unnatural" to some ears. Also, even though this might sound awkward to our modern ears, I would that the cat that lives in my house continue to stay with me.
I suppose I deliberately avoided your example (2) because I didn't have a good answer for it at the time. I like Gustavo's reply.
If any one saw a mistake in these two sentences , please enlighten me
If anyone sees a mistake in these sentences, please let me know.
I hope you see the difference. I'll be glad to discuss this further if you don't.