能 indicate the ability to do sth. eg.我能说汉语。(I have the ability to speak Chinese.) 可以 indicate the choice(ok or not ok). eg. 我可以和你一起去看电影吗？ (ok or not ok?)

your understanding is okay. but the examples are not right. we don't say things like that. 这个被子能卖给我吗？ ('可以'不用说，省略掉) 给。 这个被子可以拿给我吗？(拿过来看看) 可以的。给。

Agree with both of them. 1. 能 and 可以 can be interchangeable in Chinese interrogative sentence. 2. 能 and 可以 have a little difference in Chinese assertive sentence. e.g. 我能吃三碗饭。-----能 emphasizes ability here。 我可以吃三碗饭。-----可以 also means ability，but has got permission here.

Can 能 and 可以 be used interchangeably when asking for and giving/denying permission? Yes,they can. But, when comes to buying things, in English,"can I have ..." is a fixed patten to show politeness. in Chinese,you needn't to translate literally. We just ask directly: "我要这个杯子" “这个杯子多少钱？” “这个杯子怎么卖？” hope it helps.

我能买这个被子吗？ 能/不能。 我可以买这个被子吗？ 可以/不可以。 In this case, you have to add '吗' because this question requires a modal particle.