Yes, the level of water outside the skimmer does have a lot to do with the skimmer's performance. The inside level will never be higher lower than the outside water level so if there is not enough depth, there won't be enough water for the pump to run. In terms of water line, we have done that before and we decided to remove them as people were getting too confused by it. As you know, every system is differently so the line does not work for every system. Most systems require you to play around with the skimmer until you find the optimal spot for the skimmer in your system. If you were to move your skimmer to a second tank that is completely separate from your first system, you would not be able to run the skimmer in the same position and running as you did on the first system. You would have to tune the skimmer to that particular system and it may require you different water depth and different gate valve position.
Please be sure that you run fresh activated carbon on the system. Carbon should only be ran for 2 weeks max or it will begin to release whatever it has previously absorbed. In the case of carbon, old carbon is worse than no carbon at all.