No, you can simply purchase the Wii Remote as an accessory, and get started. No other configuration is necessary. Batteries are included!
All current Macs have bluetooth built-in. If you're not sure, look at your System Preferences for a Bluetooth icon.
You can purchase an add-on bluetooth dongle, which will connect via USB. Additional software may be required to configure it.
If there are no lights lit on the Wii Remote you've probably been caught by a strange WiiRemote framework bug. Hold On/Off on the Wii Remote for a few seconds and then try to connect with 1 and 2 again. You may have to restart WiiToMidi to get it fixed.
Because that's the way the Wii Remote is. The accelerometer sensors in the device are very sensitive and, unfortunately, very noisy and jittery. Some applications implement signal smoothing to iron out the noise. Unfortunately this can also make the control feel laggy and less responsive.
Signal smoothing can be controlled using the up and down D-Pad buttons. Up makes the output smoother and down makes it more direct.
Using the A, B, C, and Z buttons you can send four different notes: C, D, F, and A. Letting you change which notes you send will come eventually.
"Drumming" and Ocarina melody mode are on the TODO list.