When you enroll, you can select an elective. See if there is an elective tied to the cooking skill, that way your sim will advance in the skill while cooking.
For the home situation I moved in a house sitter to my sims home. When she graduates she moves back home and I will move out the house sitter.
About the home situation with the younger siblings, I would say turn aging off. Whatever you do, best not switch back home and leave your students unattended for longer periods of time, especially while the term ends. There are several people complaining about students failing class when players switch to other households.