1 ) The angles are measured from the normal to the reflecting surface (That's vertical in the illustrations). The formula given in the project discussion assumes that the diffracted beam is on the opposite side of the normal, and both angles are measured from the normal as positive values. If the incident and diffracted beams are on the same side of the normal, then one of them will be positive and the other one negative.
2 ) When the incident and diffracted angles are zero, then both sines are zero and the diffraction is zeroth order. As the angles move away from zero, then a delay occurs between the diffraction from one disc groove and its neighbors. The formula given is called The Grating Equation
. If you do a web search for that title, you'll find several discussions for how it is derived and how to use it. Example: http://www.physics.smu.edu/~scalise/emmanual/diffraction/lab.html
3 )Diffracted orders can appear in a variety of locations depending on the incident angle. You will see multiple orders, and you can check what order each one is after you get a value for d and require that m be an integer multiple for each one you see.
4 ) and 5 ) d must be a positive value. If you get a negative value, you must have the sign of an angle reversed.
6 ) If the tracks are close together or relatively far apart, how does that affect the number of tracks that can fit on the disk? How is storage capacity related to number of tracks?
7 ) Nanometers (nm) and microns are just two different units of measure. Look up how they relate.
8 ) Think about it given the other answers here.
9 ) See answer to 2)
Sorry this is late, but hope it helps.