Can I assign a different style for each category?

There is a way more complicated way to try this for numbered citations, but has some manual work involved, as you need to figure out what number a citation would be (so format them all once -so you know their numbers) and then put that information in a field that would be included in the Bibliography Layout (Put the number in the Label field for this, and replace the Bibliography no field with “Label” (no quotes). If you use this field, you may want to copy your records to a new library as you go, and then insert in your word document.   Then unformat to temporary citations (not plain text) and replace the 2nd language with square brackets, and format, unlink.  Then repeat with other output style after changing the temporary citation delimiters.  Then you would again combine the two bibliographies and sort them.