I'm not sure about the infringement, but to tye dye, you would buy rit and use it as directed (I'd suggest atleast 2 colors if not more). Then this is what I would suggest for making a mickey head (though I am NO expert when it comes to mickeys, I have done a bit of tye dying.)
lay the shirt flat on a table. Then in the center pick up where you want the middle of the first mickey circle to go just a tiny bit. grab it with a fist so that a small area of cloth is sticking out, and wrap a rubber band around it, make sure the band is really tight, and make sure there is a wad of cloth being separated from the rest of the shirt. Do the same for the ears, only make each section smaller. Then for the rest of the shirt, I'd wad it up into a tube shape, and wrap 3 or 4 rubberbands around it, leading back to the 3 wads for the mickey head.
Now, dip the 3 mickey heads in one color. (Try not to dip passed the rubberband, so that the dye stays in a confined area.)
With the rest of the shirt you can either randomly dip areas of the shirt in colors, or whatever you like. I'd suggest trying it on a cheap t-shirt (even if you have an old rag or shirt that you don't wear anymore, just to test out the method and change it up a bit if you need to before using it on the final product.)
I hope this helps! (Also, if it works, do you think you could post a picture?)
tricia.