"Can you use chopsticks?"
"可以“ ”能“ and ”会“ can all be translated to "can" in English, but they are used differently in Chinese. "会“ is used for things you learn like languages, using chopsticks, playing sports, etc. “可以” is related to permission, so if you used it here, it would roughly mean "Are you allowed to use chopsticks" which is obviously awkward. “能” relates to physical ability, like humans are able to walk, speak, etc. Hope this helps!
It is actually not awkward at all to say that in Chinese.
Please make reference to the discussion in this thread too:. https://www.duolingo.com/comment/25862075
“你可以用筷子吗？” can be used in the (A) meaning in the thread. It does not mean "allowed to"; it means "possible" so the sentence is literally "Is it possible for you to use chopsticks?" and is a way of asking about the ability. This sentence therefore also extend to the meaning of a request for not using other utensils. So if you ask for knife and fork in a Chinese restaurant and the waiter says “你可以用筷子吗？” , it would just mean a negative response. This sentence does not have the meaning of "Will".
"可以用筷子" is never used. I even did a google search for the phrase, and it's only coming up with “会用筷子”. You could only use “可以用筷子” if you maybe have a fork, but you are asking someone for some chopsticks, "我不需要叉子，我可以用筷子吗？“ or ”我们这里没有叉子，你可以用筷子吗？“ as in asking if that is alright. “可以用筷子” has nothing to do with ability.
Gentry, all your explanations and examples cannot be more correct. I only have reservation about saying 可以 is awkward or it is never used. That is a bit arbitrary IMHO, as a native Chinese speaker.
Firstly I am on the same line that beginners would better stick to 会 in this sentence. They should use words with the inherent meaning rather than alternatives with implied meaning, until they have built up basic knowledge of syntax structures and certain vocabularies and are about to venture into richer meanings and variations.
I would also like to invite you to read this thread:
where we had discussed a similar issue.
Let me use another simple example:
Camels / Do not drink water / Survive / One Month
This is not a "skill" so we don't use 会.
It also has nothing to do with permission.
In English you probably will use "Can", won't you?