This problem me feel very uncomfortable. How can I make these lines flat?
I’m trying to work out what you mean. They seem to be facing due Y, so are you asking how to point the camera due X so that they appear completely horizontal on screen?
if its the camera, enter frontview with 1 on the numberpad in case you tilted the camera by accident, then return to 3D view.
If its the line itself, you can select it, then scale it by a value of 0 along the X and Z axses.
I mean anti aliasing.

You cant do this in blender 2.79, however blender 2.8 has some AA built into it. Perhaps worth considering changing to 2.8 
Actually, you can affect the drawing of lines in viewport by adjusting the amount of multisampling in user preferences.
