Yes student can change the course with the consent of the college you can change course.

Yes it take time.All of you will get visa easily but only issue with two Adults about them you have to proof that you can afford them without doing anything.This is main point which normally arises while doing this.

Talk to home office again what status of my application and how i can get more details about this.It is only the best solution which you have.

You should take letter from your college first in which you mention that you want to change your college due to some reason.After doing all this than you will need to contact with Home office for extension.

You should apply visa for your partner while living in London this is one the best chance where from you can meet with each other.