nope, you need at least a 7D or the upcoming 60D to trigger that flash using camera body's built-in flash.
or
use one of the higher-end flash that can act as a master (e.g. 580 EX)
or
use the ST-E2 flash trigger
or
use a cheap radio trigger (e.g. yongnuo or octopus or whatchamacallit)
or
use super expensive radio trigger (e.g. pocket wizard)

2000mah is enough

The type of battery determines the recycle rate (how fast the batteries can supply electricity to the device).
Actually the battery's internal resistance affects how fast the electrons can move in the battery.

you can also try reading through this: http://www.batteryuniversity.com/

The number of shots you can take depends on your flash power that you used.
If you use your flash at full power for all your shots, of course the number of shots will not be as much as if you are using it at lesser power.

So, for all those people asking about the number of shots for a particular brand of battery: it all depends on the situation.

Why not just test them out?