Canon ZR500 battery charge

HELLO.
I just bought the Canon ZR500 and as you may know, it comes with:
1 AV cable set (yellow, red and white cables connecting to the TV useally).
1 Canon Li-ion battery pack
1 Canon Compact power adapter (mine: CA-570).

Im just askin' - does the power adapter charges the battery? Or do I have to buy a battery charger?

Thanks in advance.

Yes , it will charge battery . It's slow tho . You should get another - larger capacity battery and charger . I got mine from singertec .
It sucks to run out of power and having to drag a cord plugged into wall around .

How slowly?
Cause it was plugged in the whole night and the red charging light was just flashing a bit faster.
AND it seems as if the battery never been charged at all! If I unplug the camera from the adapter it immidetly shuts off.

So how slow? xx hours? Prehaps xxx hours? O_o

Mine took a couple hours from 1/2 charge . Check / turn on camera without adapter pluged in , if camera works your are OK . My red red flashes always too .
I go by the screen that displays how much battery is left .

well thanks for the help but i still think something is wrong with mine.
i'll buy a charger and an extra batt' like you said, dont wanna wait this whole time.

thanks again.

EDIT:
i just found out something, i plugged in the adapter to charge the battery and left it for 4 hours. the battery didnt charged AT ALL, 0%.
i notcied that the adapter and the battery wasnt even warm.
i belive i have a problem with my adapter. im testing it right now by leaving the camera on for 20 mins without the battery and see if it gets warmer.

P.S.
yes the red light is flashing when the adapter is plugged in as if it was charging.