It is possible (and even common) to add a comma after the introductory word 'however' and before the conjunctions 'since' and 'which'. However, as suggested by CarSmack, in none of these cases is a comma obligatory; here commas just serve to clarify meaning, so there are no hard-and-fast rules. So, what to advise? Your sentence is neither very short (in which case commas would be unnecessary and a distraction) nor very long (in which case several commas would probably be needed), so don't worry too much, and add commas where they feel right. [Khan is right about it being unnecessary to put a comma between main and dependent clauses, but feel free to add one nevertheless, if it feels right.]
Regarding 'emotion' or 'emotions', your phrase "the classification ... emotions" seems grammatically correct, but is certainly not idiomatic. First, the definite article 'the' is better dropped since you are making a general assertion. Second, 'research' is one of those odd words that appears only in the singular in English ('equipment' is another). Third, 'for' is not the right preposition. A minimal re-write would be, "However, it is hard to use the classification methods of research into emotions ...". Even better, the preceding sentence talks about emotion classifications and their universality, so it should be possible to say, "However, it is hard to use these classification methods to study attitudes...". This is more compact, which is another way to achieve clarity.
Finally, the phrase "which may differ a lot across cultures" could be improved. The repetition of the word 'cultures' is a sign that you should aim for a simpler and more compact re-write; also 'a lot' is not compatible with the very formal style expected in scientific writing. You have already established the proposition that emotions are universal rather than cultural, so it would be clearer to say '..., since they - unlike emotions - are strongly dependent on culture.'
Bottom line: "However it is hard to use these universal classification methods to study attitudes, since they - unlike emotions - are strongly dependent on culture."
That is 22 words instead of 30, and conforms to scientific idiom.