1) Best AF Mode: AI Servo .. This tracks focus continuously on moving subjects
2) Ideally you want to try shooting in full manual. This helps avoid having the meter get fooled. But, you need to be able to read the scene and adjust as necessary. Barring that, I'd probably use Shutter Priority so that you can keep your shutter speed up high enough to avoid camera shake (what lens, btw?) If you need a faster shutter and have run up against your widest aperture then bump up your ISO.
3) Center Focus
4) Spot Metering would give you your best reading on the bird itself (provided it fills the majority of the circle in the viewfinder) but this is why I suggested Manual mode. Then you know your exposure is correct and your camera won't be fooled by (for example) a white bird against a dark background or vice versa.
5) Good Question. High Speed continuous will certainly get you a lot of frames in a hurry but try Single Shot and see if you can get the composition you want by anticipating where the bird is going and what is in the background. Shooting with both eyes open can help you keep a sense of the "big picture" and what's around your bird.
Good Luck and be sure to post your efforts in the Bird section. Lots of really talented photographers over there! 
