For the y tick labels, just axis = (yticklabelsvisible=false,) should do it. The other two may be slightly less easy to do in a clean way.
ylabelvisible can definitely be made to work for the shared y label but yeah, I don’t think it does at the moment.
For facet labels, I imagine the cleanest solution is to support in AoG yfacetlabel.... attributes mirroring ylabel... attributes to customize it, so one would do axis = (yfacetlabelvisible=false,), but that also needs to be implemented. For now, facet labels take the styling (color, font, and size) from the axis title, which is a bit of a stopgap solution, they should probably have their own attributes.