Oh dear...... DO NOT use the bootlight as a power source. As hot eb said buy about 5 meters of power cable (8 gauge should be sufficient) and run a new line from the battery to the boot.
The fire wall should already have a grommeted hole which you can pass the wire through. Feed the wire under the carpet a run it along the side under the plastic trim thingo's below the doors. Make sure to have a fuse no more than 10cm away from the battery. The ground wire should also be the same size as your power cable (make sure you find a nice clean earth contact)
Check if the head unit has line outputs, if not then either buy a new one that has, or, if funds are low, then I believe there is a way to convert your existing speaker cables into RCA's, I've never done it before so I wouldn't know how to do it. Ask advice from jaycar, but DO NOT just stick your speaker wire into "line in" on the amp.
6 X 9's are obviously 6 inches by 9 inches, so no they won't fit since the holes you have now are only 8 inches in diameter, in fact they won't fit at all since they're oval shaped speakers. You will need to either buy some spacers or cut the shelf some more, but in either case, I recommend you use some thin MDF so that you won't have gaps were the speaker is 6 inches in diameter and the hole is 8.