I also had to replace the undertray on the Roadster a couple of years ago.
You DO NOT have to pull the bumper cover off to replace the undertray (no. 6). The undertray is held on with 10 screws that screw into piece 15 or piece 4, clip nuts or what ever they are called.
Be advised that the left or right air ducts (no. 1) may be damaged and have to be replaced. Mine were.
Three screws along the rear undertray, two on each side screwing into the clip nuts on the air ducts and three along the front through the bumper cover into the clip nuts attached on the undertray.
As for the bumper cover lower screen (no. 2) you do have to remove the bumper cover to fix this, unless you have enough room to get to the parts from under the car with the undertray off.
When I took my bumper cover off to get repainted, I removed all the odd bits. The lower screen is held on with screws, that screw into the bumper cover.
Once you get the car up on stands and you look, everything will become clear.