First thing first, don't panic! I'll try to address your questions one by one.
1) How will this help in a real world situation?
Take another good look at the Introduction of the project page. It's got great info on the Sun and radiation, and how both are necessary for life as we know it. Also, this is basically a "real world" project; radiation is the focus of study for several fields, including, but not limited to, energy and photonics engineering.
2) What's the control? Independent/dependent variables?
I don't want to give too much away, since the only way you'll learn is by figuring them out using what you already know. And I'm pretty sure you know what the control and IV/DV are, but here's a quick refresher: the control is something kept constant throughout the experiment. The IV is what you change (hmm... maybe color?), in order to observe and make conclusions about the DV.
3) I will have to explain to my class what radiant energy is. Do you have any sources I can use?
If you scroll down to "Bibliography" on http://www.sciencebuddies.org/science-f ... background
, you'll see a list of sources available for reference. Of course, by no means are you limited to just those. Do a Google search if you want to find out more, but don't have much time left!
4) I don't understand #10 of the procedure. On the HyperPhysics website, it asks me for the emissivity. I do not know how to find that.
#10 says, "Graph the power output of each square. Since power depends on the fourth power of the temperature, a small difference in temperature can cause a big difference in power output." I don't believe that, for the purpose of this project, you need emissivity. All you need is P = σ A(T^4 - (Ts)^4); refer to the project page again, under the part that reads "Equation 2." You should already have the temperatures, the area of the squares, and the Stefan-Boltzmann constant. Now just plug in the values and find the power outputs!
I think I've covered everything, but if you have more questions, feel free to ask! Hope this helped and good luck!