Yes, there is a Boss tone studio application for the SY-1000. Your assumptions are correct, you can choose to mute some strings and not others. The FX banks can be dragged around to whichever part of the signal chain you like. I'm not sure about pickups as I've only used the GK-3b, but I'd ask here:
https://www.vguitarforums.com/smf/index.php?board=321.0