A. Yes, by using the search:
process_publisher_state:FILE_SIGNATURE_STATE_UNSIGNED

B. Yes, by looking at signed and unsigned executables in the environment and seeing if another difference can be found, thus locating unsigned files in the environment.

C. No, it is not possible to return a query for unsigned files.

D. Yes, by using the search:
NOT process_publisher_state:FILE_SIGNATURE_STATE_SIGNED