Shouldn't solar cells be nonreflective? If solar cells take energy from light, then why do they reflect it? How come they can take energy without actually affecting the source?
Shouldn't reflected light (as a minimum) have a lower frequency?
Assume that there exist a "perfect solar cell" (i.e. one that takes 100% energy from light). Shouldn't it be nonreflective?
 A: Good question!
Solar cells made of silicon are naturally quite reflective (30%), and there is quite an art to making them less so - because any sunlight reflected is not available for power conversion. Antireflective coatings are not easy to make since they tend to work best at one wavelength and angle of incidence; you try to make them so the total power extracted from the sun will be greatest, but that may mean some wavelengths will be reflected. Note also that the reflected photons typically didn't make it into the silicon - in other words, the solar cell didn't extract some energy and reject a lower energy photon.
At this website you can see a more detailed description - I will just reproduce here the plot of reflectivity for "no coating", "under glass", and "optimized" coating. As you can see, a lot is done to mitigate the problem, but as mmesser314 pointed out, even things that are almost "perfectly" (99%) black will reflect 1% of the light, which is quite enough for the eye to pick up.
 
A: It is hard to make anything be truly black. At any frequency, some light will be absorbed, some reflected, and some transmitted.
Eye response to light is logarithmic - We can see bright light, but also much dimmer light. So if 99% of the light is absorbed, that still may not appear black.
Smooth surfaces produce a mirror like reflection. If illuminated by the Sun, all the photons arrive from more or less the same direction. They have the same direction after reflection. If you eye is in the path of the reflected light, it receives all the reflected light. This is much brighter than a diffuse reflection from a rough surface, where light is scattered in all directions, and you only receive a small fraction of the total. 
Typically, reflection does not change the photons. It just reduces the number of them. If the reflected light is redder, it is because bluer photons were absorbed. 
A: How come they can take energy without actually affecting the source?
Well the source is the sun, so it just sends out light and it doesn't matter where it goes, the sun will keep out sending out light, so it will be sunny tomorrow, amd the next day and the next day.....it will keep on going for a long time
Shouldn't reflected light (as a minimum) have a lower frequency?
It does. The light from the sun is actually a range of frequenies and the solar uses some of these frequencies to make electrical energy.   So the light coming in to the solar cell gives up some of its energy into the cell and the light reflected from the cell is at a lower frequency because it has lost energy. 
Assume that there exist a "perfect solar cell" (i.e. one that takes 100% energy from light). Shouldn't it be nonreflective?
Sure, we would love to make a solar cell that good but we can't and yes it would be non reflective because all the solar energy going in would stay inside the cell, none comes back out so no reflection.
