Lots of questions (related to this Meta discussion). I will just tackle a few points I feel confident about answering.
Subfloor
The Schluter DITRA does not need to be on CBU so I would skip the 1/2" layer of cement board you are planning on using and make your plywood subfloor thicker (or just skip the CBU and keep your 23/32" OSB). CBU is not "stiff" enough to be a subfloor, it can be used instead of DITRA but it must be secured to a subfloor. It rarely makes sense to use 1/2" on the floor unless you are trying to make the finished floor come out to some specific height (for example to help the transition to another room with a different floor). If you are not goin gto use DITRA, you will want some CBU on the floor but the 1/4" stuff is fine.
Apply the modified thinset and DITRA directly to the plywood subfloor. Checkout Schluter's DITRA Installation Instructions for details on the subfloor prep and how to secure to DITRA to the plywood.
Toilet
Without a picture or diagram it is not really clear to me exactly what the issue is with the toilet drain, but that won't stop me from taking a guess :)
You may be right about getting away with cutting a larger hole in the subfloor to handle the bend of the toilet drain pipe. Are you sure the PVC drain will stick above the finished floor? Realize that the thinset between both the subfloor/DITRA (not very much) and DITRA/tile (more so) will add a little to your height, maybe between 1/8" to 1/4".
Have you measured the height of the toilet drain with the flange installed (just dry fit it to take a measurement)? The flange can be installed on the top of the finished floor (tile), on top of just the DITRA, or on top of the plywood subfloor. In your case you would probably want it as high as you can, so install the tile first and then glue the flange to the PVC closet bend. I think once you dry-fit the toilet flange you will see you are OK here.
Prescriptive nailing schedules are part and parcel of flooring or wall exteriors. In both above grade situations, the goal is to create a unitized structure. Wall panels properly attached become stressed members that resist lateral racking forces.
In the basement, over a poured concrete slab, no structure enhancement is necessary. Therefore any fastening that produces a secure, trip free (smooth)surface is the goal.
It somewhat depends on what the final surface will be. Floating laminate floors would work over floated ply. Heavy cabinets or a workshop might work better over a more secured surface.
Best Answer
Vinyl is a material that takes millennia to degrade. It is waterproof and is resilient enough to .walk on comfortably. It would be wise to leave the vinyl and build directly on top of it. Typically, when installing a floor in a concrete basement a vapor/moisture barrier is installed to keep the materials above it dry. Can you clarify why the vinyl would add to the slope (of the floor?)? Are you concerned with the floor being raised enough to interfere with the door bottom? If so, it is relatively simple to trim the door bottom.