Check with your own rules etc.
That said:
1. Dual is not normally multi-pilot. Multi-pilot is for when you operate as part of a multi-pilot crew on an aircraft certified to be flown as such. For example an airline jet that has a crew of a first officer and captain. Log dual as single pilot.
2. It would depend on how your logbook is laid out but I would think that single pilot + multi pilot should equal total time (you can only be one or the other). My logbook doesn’t distinguish between single pilot and multi pilot though, that is implied by the aircraft type.
3. I can’t think of any. If you are dual then you are the student, not the PiC.
Again, you need to check your own local rules and customs, they may be different.
If you are ever confused about logging PiC, remember that there can only be one PiC and ask yourself what your instructor would have logged. You can’t both be PiC.