Yes, you are right, the requirements are also in the file of the battlemage, but this requirements are for this command. To be morphed, the requirements for the command and for the unit that is going to morph to must be met. That way you can make more than one type of unit morph to the same unit and have different requirements. Usually command requirements are used for attack commands, for example in the Archmage.
Yes again, you can morph to any kind of unit.