"I can't speak Chinese. Luckily my friend can."
I agree and I think Han4yu3 is a better translation for spoken Chinese than 中文. Unfortunately, I couldn't even report that the "correct" solution is unnatural.
汉语 applies to mainland China only. As we don't know the context, 中文 is better since it concerns all kind of chinese language spoken worldwide.
As far as I understand, 能 refers to innate abilities whereas 会 is used for learned abilities such as speaking languages - is this not the case?
i would add that 能 frequently shows permission, or the intervention of circumstance. that was my first thought when i read that sentence, that the speaker wasn't allowed to speak chinese, not that he or she lacked the ability.
I don't think that was the intention of the writers of the sentence, but I believe you're correct that it looks a lot more like it's talking about permission.
Yes it does have that meaning of permission as well, but I would translate it as able/not able to. The context will generally imply whether they are able/not able due to lack of knowledge, time, circumstances, or permission, such as not being able to reveal a secret.
好在 is not a valid translation for luckily in this case. It should be 我不能说不通话，幸好我的朋友可以。
It is nothing but Cantonese to me. Maybe it had become Mandarin today, but it certainly was not acceptable in older days.
Actually it IS valid. It's better to regard 好在 as a common phrase instead of 好 + 在.
What on earth is 好在... I've been speaking Chinese my whole life and I've never used in conversations... Normally it would be 幸好...
Does the appropriate use of 不能 vary between region it is spoken in, or the various contexts in which it is spoken? I remember hearing it used for both permission and ability, but didn't ever work out if there was a rule for appropriate use?
会，能，可以 会：我会说汉语一点儿。I can speak a little bit of Chinese. (let's try) it express the future as some proposal 能：我不能说中文。I haven't the ability to speak Chinese. (Use another language). 可以：我不能说中文可是我的朋友可以. I don't speak Chinese, but with the help of my friend we will get it. (please address to him)