The connection lines do not change color when I select another color in the "View Configuration" panel. I can turn them ON/Off by pressing the "Eye" button. So Why doesn't the color change?
Changing the color square in the View Configuration panel only affects new nets added to your design from that point forward. It does not affect current connection lines. To change the connection lines color for your existing nets, you will need to use the PCB Panel.
Click on the Panels button ► PCB ► At the top of PCB panel choose Nets from the pull down list ► select All Nets in the panel below. The list of nets will populate in the section below. Select the ones for which you want to change the color, then right-click on the selected Net(s) and choose Change Net Color, select the color you want, and click OK