Having your roots exposed to light wont necessarily "damage" them. It will however caused the roots to develop chloroplast and photosynthesize. This may in some plant correlate to a reduction in the roots capacity to preform tier normal function in the organism. This is according to my botany professor. That algae may just be the root turning green, could easy be actual algae though.
I used to use Styrofoam cups because they are easy to make drainage holes in and you can rip or cut them along the side to carefully remove the plant later.