Digital BW, The Print

I guess I started this thread but I probably messed up my question.

I am experimenting with duotones and quadtones for printing b/w images on my
CanonS800 (with standard color ink tanks) from digital camera color photos.
I am only using duotone and quadtones that are blacks and grays. Now maybe I
can restate my questions.

When saving the duotone image in Photoshop, is the image saved and printed
in Photoshop's native .psd gray format or is it converted back to RGB before
printing.

If it is left as a duotone image in the .psd gray format, is there a
standard or preferred Photoshop working space gray setting (e.g. dot gain
20%, gamma, etc.) given that I use an inkjet printer?

Thanks for your patience and help.

Fred Rothenberg