[Electriclight]

Ok, you have a XLR cable on left MIC channel. Is it a microphone? If so a dynamic willl not need phantom power but a condensor mic will. Set that button on the Tascam accordingly.

Put the MON control on the Tascam in the center for now.
Put the INPUT L control to the center as well as the LINE OUT to the center position.

Now in Cubase, open the Device menu to VST device control panel (This is probably not exact term) I'm working from memory.

But there should be a drop down menu where all the drivers are selected. Make sure you have chosen the Tascam ASIO or something similar (again I'm guessing).

Now you say you have set up the inputs and outputs... Hit F4 and tell me what you see. You should definitely have a stereo output bus active. You should also have set up a mono left input and mono right input as well as a stereo Input. But for right now it sounds like you have a stereo input. (That still should be fine, you just will have a wave form on only one side of a stereo signal.) Make sure it is active.

Create an audio track and assign the input to whatever. If you only have the one Stereo input it should already be selected. Make some noise with the mic and see if there is activity on that track with the meter. If not, press the Monitor button, it looks like a little speaker. Did that make a diffference?

When you play the track that you recorded, where you can see the wave form, try pressing the monitor button to see what difference that makes. Make sure you have not muted the track with the mute button and don't solo any tracks for right now.

I think you just need to understand the monitoring functions and the level settings. For example I don't understnd your line about the live signal disappearing after recording. You should only see activity on the meter (in Cubase) when there is an input and only see activity on the output meter when there is an output.