The plastic wrap clings so its not horrible. Just annoying when trying to remove it with my hands full, since it likes to stick to itself easily.
I never thought of picture frame glass. There was a buy separately cover, I believe, that was glass. However it sits really close to the water on a built in ledge thing on my tank. I was definitely worried about oxygen, and the fact that it didnt leave room to stick the heater cord through.
I dont currently have a lamp on him. He sits by a north facing window so he gets lots of natural light but no direct sunlight. When it gets dark I just turn on my room light till about 11pm. I'll turn it off then so he still gets the day/night cycle. I have an LED light in my room as a low light. So its not completely dark in my room (yes I have issues with complete darkness. Its best not to ask the reasons. lol).
I'll look into a lamp if I decide to do live plants in the other tank.