How can I get the power connections (+12V, -12V and Ground) in the schematic and on the pcb, so that they get connected on the pcb automatically?
I also have a problem with connections for cables going to the plate of the synth module.
How do I get single “connection”-spots into the schematic and the PCB?
Typically by placing a connector part in to the sketch. There are a variety available in the core parts bin from .1in headers or for power from wall warts there are coax barrel connectors available. It will depend on how your power supply connects to the board. Same with the cable connections either .1 headers to the actual connector or 1/4 inch or 3.5mm audio jacks (pc mount) are available. For the .1 headers
drag the first icon in connectors in to the sketch and then in Inspector (the lower right window) you can select type and size (but only after the part is dragged in to the sketch) to set what you need.