Welcome to the forum.
My answers to your questions are:
#1 - the camera should tell you how many shots it should hold. Other than that my answer would be -- dependingo n the size of the file that the camera creates in that format you are looking at around 300 - 1000 shots (I have no idea the file size or resolution you are shooting at so it's a guess on my part)
#2 shooting with strong backlight will require similar strength in the flash in the foreground to prevent the sillhouette. Set the flash to full and let 'er rip.