In most receivers the + POS. (red) and - NEG (black) are common to all channels and to provide power to any device plugged into them. Only the "S" Signal pin is unique to each and is used to send position data also to anything plugged into it. These wires are normally white, yellow or orange with newer systems.
Some lighting systems will also have a signal wire as they can alter functions depending on signal to turn on landing lights, change pulse rates, etc. I imagine your basic lighting does not have anything plugged into that pin and will be limited to just the red and black.
Most should do nothing if plugged into the receiver the wrong way. This will still have the red correct, but the NEG will now be plugged into the S pin. Cannot guarantee no problems, so it would always be good to double check before powering it up by confirming it's the same as the other channels.
As for power, I would recommend a separate BEC as the easiest and best method to fix your problem. They are very inexpensive now and have some good ratings. In fact, I run all my helis this way as their flight control systems are so much more demanding. If your current ESC lists the BEC output grab one of greater current rating. If you really want to be sure a 6A should more than cover you.
They do take a bit of work to install. First would be to eliminate the current onboard BEC by popping the red lead in the plug from the ESC to the receiver and taping it back or covering it with heat shrink. The new BEC needs to be soldered to the existing battery connection so it gets power when the battery is plugged in. If you have a spare channel in the receiver simply plug the BEC output into that and go flying. If not things get a bit more complex and I would try to cover that in another post.
As for cooling there are a few little tricks we commonly use. One unobtrusive inlet is what is called a NACA duct. Have a boo here and you will see what I mean.
I also included a pic of one in the nose of my Polaris. The floor of the duct has not been installed yet.
Another very easy way to make either an inlet or outlet, (or both) are plastic spoons. Simply cut the end in half, sand the edge and use the forward part as a scoop covering either an inlet or outlet hole. The second pic shows an example of that.