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The by-country subcats should be deleted. Categorising languages by country will cause massive category clutter on the more widely-used languages, such as Arabic, English, Spanish and French
For the most part I support BrownHairedGirl's suggestions, with a minor caveat and an addition.
Caveat: I'm not sure the addition of the word "language" to category names is necessary. An explanation on the category page, like that at Category:English words may suffice, perhaps strengthened a bit (e.g. "Articles that are about Spanish language words, not words associated with Spain or ideas described by Spanish words").
Addition: The explicitly "by culture" subcategories should be somehow reorganized. Maybe the easiest way to do that is to remove them from this category altogether and make something like Category:Names by culture into which the surnames and given names subcats (and maybe Category:Native American toponymy, too) could be moved.