Answering the second question first, yes, you could keep all of the component parts in a single file. But depending upon the printer driver software you intend to use to print your creation, you may have to export the various parts out individually to separate files for printing purposes.
Looking at your blend file, and your question, your proposed 3D object will not print very well on the 3D printing systems I am familiar with, if subdivided according to the illustration in your question.
The first challenge I see is your stated proposal to use a "square pin ... and square hole". Depending upon how you intend to orient the pins and holes, I see this as a potential challenge because 3D printers do not print horizontal "square holes" well. You'll need a different method--or methods-- of joinery.
The second challenge I see in the ~.blend file I downloaded is the slot in the ring opposite the two "ears". The slot is a "hole", which again, cannot be produced on a 3D printer.
The third challenge is in the shape of the ears. The 3D printers with which I have slight familiarity require a flat surface on which to form the object to be printed; they can't print an overhang.
In the absence of information on the intended size, this image
(source: core.com) shows how I would divide the item for 3D printing. First, I'd divide the item in two along the vertical plane shown by the blue line in both sides; then I'd further divide the item along the plane shown by the yellow line, creating four sections: two of the half with the ears, and two with the half with the slot. I'd place the two sections with the ears so that the part of each section co-incident with the yellow horizontal plane is on the printer bed. With the half with the slot, I'd place the two sections with parts of the slot on the printer bed so that the outside of the piece is along the printer bed.