If the PIC had a restriction on his/her BE300/350 type rating "second in command required" you could log SIC because a SIC is FAR required. As far as recieving "Duel" for your ATP, unless you are in a 135/121 operation (and the Captain mostly never signs a log book) you need a CFI ME to sign your log book and record the "Instruction".
JAFI
JAFI