1) The spoiler has a green wire and a black wire coming out of it and the hole on the bootlid has a green wire and a black wire coming out of it. Is it just a case of joining green to green and black to back?
I'd assume that yes it is that straight forward. If you have a green and a black going to a green and a black, seems like a no brainer. If it doesn't work, try it the other way. You won't hurt anything by doing so.
2) In terms of safety(getting shocked) will ensuring ignition is off be enough?
There should be no worry about shocking yourself. There's not enough voltage in the system. No power is going to flow through the wires if the brake pedal is not depressed. At this point, neither you nor your car is in any danger.
Make sure you completely seal the connections on the wires. If you don't the power lead could potentially ground to metal. While this won't cause a fire or anything, it's called a dead short and will blow the fuse. It's easier to take care of it now while you are putting things together rather than try to figure out what the heck is going on later.
With regards to the water, just do your best to get all of it out you can. A little bit shouldn't cause you huge issues, but you do want it dry inside. Water may want to deteriorate things inside of the spoiler. You might try blowing warm air through the spoiler like with a hair dryer on a low setting. You don't want high heat because this might melt or distort something.