Is it possible to add and remove fields from the user profile? For example I want to add a field for LinkedIn profile and remove the Schools field.
For adding and removing field to the User Profile you can do that via Central Administration ->Application Management -> Manage Service Application -> and click on the User Profile Service Application -> Manage User properties.
I strongly advise against removing any ootb user properties cause it might break your SharePoint 2010.
Hope this helps.