Sure. I mix them all the time.
Not sure if you are a pre-washer or not, but batiks and tie dies (especially tie-dies!) can be real bleeders. I usually wash my FQ's in the kitchen sink and agitate slightly with a wooden spoon. Put like colors with like colors, use HOT water (which is why I agitate with the spoon instead of my hands), a small amount of soap, a color catcher and/or synthrapol. Rinse well, and repeat! Some of my batiks and tie-dies will take 2 or 3 washings before I am satisfied the bleeding has stopped.
As for suggestions on how to use them together ... would have to see the pic's of the fabrics. But use them with prints just like you would use other prints or solids.