I agree with Michael, but there is something wrong with the expression "the most different kinds of products". It does not "read English" and therefore does not make sense. Do you mean to say, "among the countries producing the most diverse range of products"?

It depends on your meaning. Do you want to emphasise the ability of countries to produce? If so, use "can". But if you just want to define the group of countries, there is no need for "can", and either "which produce" or "producing" would be correct.