The compilation of the binary on the Raspberry Pi target using the Raspbian Lite and the data exchange via shared directory is just one possible way - maybe the simplest one... It is described in the document Getting Started with Raspberry Pi. Nevertheless, there are other options - e.g. using a cross compiler to create the binary and then transfer just the binary to the target.
Let me answer your questions:
A1.) Yes, this should be possible - but I did not test it.
A2.) Yes, of course. In case you have setup a cross compiler environment, you do not need a shared directory between PC and Raspi. Then you need only to transfer the binary.
A3.) It is just the binary.