Important questions regarding Harbis and Dar al-Harb, etc.

[a brother]

As-salaamu 'alaikum brothers and sisters:

I have some questions regarding harbiyoon (harbis), Dar al-Harb, and related matters regarding this topic, and am hoping someone can please help address some of these important issues, insha'Allah.

Who are the harbiyoon (harbis) exactly? Are they the disbelieving "noncombatants" (civilians) of countries who are at war with Muslims? To clarify, if certain disbelieving governments are at war with Muslims or Muslim countries, are the noncombatant disbelievers considered to be harbiyoon, even though they are not part of the government or military infrastructure of these countries? (and presumably they obviously don't all agree with everything their governments are doing)

I have heard that there are basically two categories in which the classical scholars described the world: Dar al-Islam, and Dar al-Harb. Is this correct? I also believe that there are "subcategories" in which Dar al-Harb can be further divided into, such as Dar al-Ahd, meaning I believe, that the disbelievers have a treaty or a pact with the Muslims. Is this also correct? Can the disbelievers of these countries ever have a treaty or pact with Muslims (and vise versa) even though their governments are fighting Muslims?

Also, how are Muslims living in the West supposed to be categorized? Does it change if that government is at war with Muslims or fighting Islam? Can Muslims ever be considered "harbis" in any way, in any shape or form while living there?

I know these are a lot of questions, but JazakAllahu Khair in advance :)