Advisors are part of the squad the are assigned. Always starting from Command Squads filtering down the chain of command (Command HQ, Platoon HQ, IG squds, etc).
Commisars can start as independent characters with the correct doctrine but paying an extra ten points on them is just silly.
In the IG book they are not designated squad upgrades. They are assigned and become part of the unit, hense increasing the target for half strenght. In the basic list only independent character are the officers.
Yes lone surviors Commissars/Priests/Psykers have to take all-on-their-own tests after the squad is kacked.