Translation:Sorry, we can't refund it.
I can't speak to the Chinese meaning. The English translation is fine, "we don't offer refunds" and "we can't refund it" are not completely interchangeable. A store may offer refund policies, but refuse to refund if you misuesed the product, broke it and then tried to get your money back.
My own sense is that it's not commonly used intransitively.
Even so, "we can't refund it" is still a little weird, because the "it" has to refer to the purchase price, not the item being returned, and we would have to imagine a specific preceding sentence like "can you refund my money", whereas it's more likely that someone would say "I'd like to return this" or "I'd like a refund".
"We can't give you a refund" would be better, I think.
No, while there is overlap between the meaningsof 可以 and 能， the negatives are distinct. 不可以 means 'permission is not granted' while 不能 means that it is impossible. See explanation here: https://resources.allsetlearning.com/chinese/grammar/Comparing_%22hui,%22_%22neng,%22_%22keyi%22.