Are there food-food (such as drug-drug) interaction between turmeric, ginger, sage, and rosemary if they are mixed together?

That sounds like an interesting combination of taste... These are herbs and spices, and I wonder how much of it you're combining?  What's the dose?  Traditional herb texts recognize 18 herb-herb interactions, particularly with aconite, licorice and veratrum.  To this date, I haven't come across any herb-herb interaction between the ones you cited.