I'm new to woodworking so hopefully this question falls within this exchanges guidelines, please advise if not.
I'm trying to drill the screw below into plywood as shown in the photo:

There will be a block of wood in the slot in the above photo that I worry will split if I don't drill a pilot hole first. The only issue is that my drill bit is not long enough to make it all the way through. As shown below:

So I realized that I need to buy a new drill bit but I am struggling even to do that. My drill (shown below) seems to only accept hex shaped drill bits which drastically limits my selection.

These are the screws I'm trying to drill, they are 12 x 3 inches long, shown below:

Why are the screws listed as size 12 but all drill bits are listed as fractions as shown here? How am I supposed to know what size is correct? And moreover, how can I tell if the length of the bits are at least 3 inches none of the packaging seems to list length, only the size as a fraction. :
To complicate matters, I want the screw to be perfectly flush so I believe I need a countersink to do that properly, I've been looking at the countersinks below I can't tell if the bits are at least 3 inches or whether the width is correct.

I am totally overwhelmed at this point - which drill bit should I be using?
