First did you use Anti-wilt?

Second yes cover the tub clear is not a good idea, not only will alga grow but like it was said young roots don't like light.

Third - You have roots showing. The first picture shows the structure of how they form. Right now in this stage the roots are still inside the stem but if you look close enough you can see them. As the plant matures and grows the moisture requirements increase and then the plants searches for more water. Thus you get the roots sticking out as the stem transforms into it's own plant.

They look like they should be fine.

Last - What is the temperature of the water, and are you using any nutrients at all? You do know you are taking a cutting from a plant that has nutrients so you can root clones with a very week full NPK nutrient mix.....very week like about 200 ppm.