The thing with two wires on top of the boiler is most likely a thermal cutout - if the boiler overheats it is supposed to cut the power and stop the machine heating.
When you can't see the water level in the sight glass, it can either mean the sight glass is completely empty or completely full. Sounds like in your case it is probably completely full.
The pipe to the bottom of the sight glass can clog up with scale, which prevents the actual boiler level being indicated in the sight glass - what can happen when the level probe is fitted to the sight glass is that the machine fills the boiler but does not stop filling until the level gets high enough that the water suddenly fills the glass via the upper pipe and registers on the probe. If this happens draining water from the boiler via the water tap won't trigger the machine to refill the boiler, as the water in the glass is trapped there by the blockage in the lower pipe, and the probe thinks the boiler is still full. You can test if the autofill is still working by disconnecting the wire from the level probe - after a couple of seconds it should start to fill, and connecting the wire back to the probe should stop it again after a couple of seconds.