I have my CFI right now, and I'm flying with a CFII in preparation for
my CFII checkride. Do I log that time as Dual Received, as well as PIC,
or just PIC, or just Dual Received? Also, as a CFI should I be logging
the time I fly with my MEI for my multi rating as PIC, or is that
stretching it?

While we're on the subject, how should I log my students? I have one
who has his private, and is just flying with me to build time for his
instrument rating. Should he log our time together as both PIC and
Dual, or just Dual? I have always thought you either logged PIC or
Dual, never both; but lately I've noticed others doing both, so I
thought I'd just ask.

By the way, if it means anything, I instruct at a Part 141 school.