I didn't think my description was all that great, I should of stayed mainly on the tech aspect. I can focus on the woodworking aspect.
Here are some things related that I would like to focus on for now.
1. I would like to know if there is some DIY kit or some who has built a powemat charger that can work for any device. I kind of understand the basic idea of it, just can it be done.
2. If not, I'll just go along with making a small solar panel charger.
I don't know if there is a DIY kit, but you could make one, although it'll probably be impractical. The powermat works by having a wire coil in the powermat that magnetically induces an electrical current in another coil that's hooked up to the phones charging circuitry. The hard part in making one for yourself would be making the second coil that attaches to the phone's charging circuitry.
I would like to make the finished product do three things, radio, the aux to play music on my android, and to charge my phone.
A way you may want to go about building this is to divide it into four components: the radio, the speakers, the aux/radio selector, and the charging system. You could use a kit to build the radio, or if you're feeling especially adventurous, build one from scratch. There are guides to building speakers if you want to go that route, or you could integrate store bought speakers into your project. Since the aux/radio would be using the same speakers, you'll need some mechanism to select the source: you could just use a simple switch, or do something fancier.