I am not 100% sure what you are looking for.
Every 2D CAD program I have used has the ability to turn layers on and off. My go-to one (FastCAD) also allows me to import images into a drawing so I can see those images along with any or all of the layers I am creating. I have never checked, but there must be other 2D CAD programs that have this functionality.
If you are talking about PCB design software, while layers can be turned on and off, I don't know which ones allow the import of images, but I am sure some must. Nor have I seen any that allow translucent layers. But I have had no problems working with the traces on the various layers.
You seem to want a translucent layer, perhaps for the imported image. Paint.net allows all layers to have their transparency set from 0 to 100%. It can certainly import images and it has much of the fundamental capabilities of Photoshop for the manipulation of those images. It also has a grid capability so you can do PCB design work but I do not know if it can generate the Gerber files. Perhaps it will help. I have designed complicated PCBs using a CAD/graphic program first and then manually copying the results to a PCB design program.
Again, I am not sure what you mean by "various graphic combining operations". Most of these programs allow layers to be turned on and off so graphics on them can be combined. In some cases, a graphic can be assigned a transparent color so they can cut "holes" in the contents of other layers.
Your best bet may be to take advantage of the free trial periods offered by some programs.