Lets keep this simple.
You want to get signed of for VP prop and retractable gear. This can only be done by a FI.
There is no specified time or content for the differences training so the FI will wish to see that you are competent before signing your log book. In most cases this will require sufficient GH to allow you to handle the additional engine levers and show that you understand how both systems work.
It will count as the Dual Flight, and as you quite rightly say, if the FI is an examiner he can sign your C of R at the same time.
Log as Dual and instructors signature in your book is all thats required.