As a new investigator, it is ususally best to start your own thread in order to get help. I'll ask the moderators if they can split out your question into a new thread.
I'm glad that you found an existing thread on the project to attempt to find out your answers regarding http://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p011.shtml
Take a careful look at the picture under the Experimental Proceedure section 2). Making Measurements above subsection b. The image above shows how to mark and measure the angles.
The Thetai incident angle was chosen to be -20 degrees (20 degrees right of perpendicular) in this example based on where the laser pointer was placed. Theta0 (for M=0) will be at -Thetai by definition (which in this example will be 20 degrees left of perpendicular). The m=-1 and m=-2 (and all negative m's) will be the difracted beams that are right of the m=0 reflected beam and should be in numerical order. In this case m=-1 is about -26.5 degrees right of m=0 and m=-2 is about -53 degrees right of m=0. Note: They should be precise multiples.
The m=+1 refracted beam should be to the left of m=0 by the same number of degrees as the m=-1 is to the right. In this case it shows up 28 degrees left of m=0. This means that there is probably either a slight offset in where the protractor midpoint is lined up (picture shows protractor slightly right of where the beam strike) or the protractor base is not parallel to the CD/DVD surface (picture is a bit of an optical illusion because of the angle of the graph paper, the angle of the backing board, and the way the edges of the cardboard spacer and CD/DVD show up and the edge of the cardboard spacer not being perpendicular to the backing board so judging it is difficult) or both. Even when you are extremely careful to avoid "parallax" and other things that can affect these measurements, there will be measurement uncertainty and error so don't expect perfection. This is why you should attempt to make several measurements at different points on the CD/DVD and tear down and set up the aparatus each time and average the results.
Hope this helps.