"With" and "at" are interchangeable in that context, but "were the smallest producers" should be something like "produced the least."

Yes

"With" and "at" are both fine. The thing that confuses me is that you mention three locations but you give only two numbers. Perhaps you are grouping South America and Central America as one place, but that is not clear. To make it clear that you mean two places, use the number "two" and change conjunctions or punctuation: "Africa together with South/Central America were the two smallest ..." Also, you need to omit "that" from your question and you need to say "Is it" rather than "it is": "Is it ok to write: "Africa..."...? If you choose to say "that", then do not use quotation marks.

Yes, the sentence you provided is grammatically correct and conveys the information effectively. It is acceptable to write: "Africa and South and Central America were the smallest producers, with 15.6 and 16.4 million tonnes, respectively." Regarding your second question, you can replace "with" with "at" in this context, but it slightly changes the meaning of the sentence. Using "at" would imply that Africa and South and Central America were physically located at the locations where those tonnages were produced. For example: "Africa and South and Central America were the smallest producers at 15.6 and 16.4 million tonnes, respectively, and their combined output accounted for only a small portion of the total production." This suggests that the production of 15.6 and 16.4 million tonnes was specifically happening in Africa and South and Central America. On the other hand, using "with" as you did in the original sentence, implies that Africa and South and Central America were associated with those tonnages, without specifying their physical location: "Africa and South and Central America were the smallest producers, with 15.6 and 16.4 million tonnes, respectively, contributing to the overall global production." In most cases, "with" is more commonly used when discussing quantities or amounts in a sentence like this. However, if you want to emphasize the location of production, using "at" could be appropriate.