So you do have audio signal, but it's all at 0V ? Is your multimeter set on DC voltage ? Does it have some auto-range feature ?
I guess if there is a good audio signal, it should be ok... You should probably focus on the soldering side.
P1, P2, P3 are the boost footswitch pads I think. Do you have the same readings, 0V at Q4 pin 3, if you try to press the boost switch on and off ?
I am using this soldering station, running at 400°C, from a local store :
Station de soudage numérique NEDIS Station de soudage digitale 48W SL30.
rer-electronic.fr
A bad soldering iron will certainly be harder to handle, but I think practice is also very important to improve our soldering skills. At first, I did some mistakes too, with the same iron. A fine iron tip is helpful too. If the tip is too big it will be much harder.
Edit : I know Hakko is among the best soldering tools brands.
About multimeters, I have been told to get a VC97A model, it's cheap and it's perfect. It can read Hz, which is useful with modulation circuits.