[Mondial]

The red unterminated wire may be what is referred to as a gimmick capacitor. The capacitance of the loose wire is sometimes used to neutralize the coupling between the oscillator and RF input of the converter tube, preventing interaction at the higher SW frequencies.

The lack of volume does not necessarily mean there is a problem with the volume control itself. Rather any number of problems in the various other circuits can cause loss of gain and resulting low volume. As long as the volume changes smoothly as you rotate the control, then its probably not the problem

What are you using for an antenna? The fact that the volume increases when you touch the tuning capacitor may indicate problems with the antenna coil or RF amp stage. There could also be a problem with alignment of the antenna, RF and IF stages.