No you do not have to inject data. The data should run all the way through.
When you inject power, remember that you have to also pass through the ground wire through all the pixels. Only the Positive side of the power do you seperate.
Yes as long as it is coming from the same power supply.
If you are using different power supplies than you must have the + line separated and only the ground line running through
There is a couple great pics of this in the ACL101 manual
The P2 does need a power source. It does not pass enough power to run your pixels.
You can run the P2 from the same power supply as the pixels as the power draw for it is very low.