Anyone who believes really, from his heart, in God and accept Muhammad as a prophet, he's a Muslim. However, if a person declares his Islam without really believing in the principles of Islam, he's considered as an hypocrite so he's treated as Muslim because his appearances show his Islam and he's going to be in hell. It is so hard and not permissible to declare a Muslim, non Muslim except if this Muslim declares himself as non-Muslim. However, we should make sure that this declaration was not under pressure.
About the second question, all the schools either the Sunni ones or the Shiite ones share the same pillars, the same fundamental believes and principles. So they are all part of Islam, and all the disciples of these schools are Muslim.
[Note: Islamopediaoline.org has other records archived that pertain to this topic, search: The Amman Message.]