Yes, there are multiple parts to the switch. In one position the top 2 rows are connected, in the other the bottom two rows. Reflow the switch or make an audio probe to check it out.
No worries. It is possible to board mount them. I chose not to because I’ve found that the pots will pull up the traces more often than not. I suppose that, if there were 4 pots evenly spaced, it might work better.
It could be literally anything. Check your resistors and your capacitors. The polarities look good. Look for solder bridges on the back side. So you have power in all the right places?