Partition Imported Geometry

I'm trying to partition a geometry that I've imported from Solidworks. I've introduced a workplane and drawn a rectangle where I wish to split the geometry to obtain different domains. After this I tried converting the rectangle into the solid, however keep getting an error that says, "output object is empty".

Also can I refine a mesh within a single domain? The purpose behind partitioning the domains is to refine it without any hassle.

Would appreciate any help. I'm kind of new to this.