For an extension for my led strip, I simply cut the wire leading out of the control box, and wired in 12 ft of wire from an electrical supply store. The wire I used has 4 separate wires inside, because I only have rgb, not rgbw.
Did you remove the plastic cover over the remote battery? It comes from the factory with plastic on the battery so the remote won't work until you remove that. The battery itself may also be dead.
I myself would skip the WiFi bridge idea. In theory it sounds cool, but you're adding more and more complexity to the system. All these components are extremely cheaply made Chinese electronics, they're not exactly reliable (I've replaced a few components of my system already). Adding even more cheaply made Chinese electronics is asking for trouble in my opinion.
