Could you please lend me your pen? All of them are polite requests. In general: could you …
No. Both are 100% grammatically correct and natural. While "could you" can mean "would …
If you say the cat might/may/could be dead you are not 100% certain. If you say the cat can be …
"Could you do X?", literally speaking, is asking a person if they could, hypothetically, do X, or …
To my surprise, I found a similar conclusion in COCA, could you please help me: 6 hits, could …
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