How to use department so that opportunities auto move when the department changes

I'm a new user, and am frustrated on two issues:

1.  When you move an opportunity from one account to another, the products and other objects attached to the opportunity do not move to the new account.  Is there a work around for this?

2.  We use departments on the user record.  When we change the department, do we have to manually change each opportunity?  What happens to the products and other objects attached to the opportunity?  Do they move automatically, or do we have to manually change them??

3.  Is there a way to set up the user records so that when they change, the opportunities and other objects reflect the changes on the user record?