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Great questions! Let me see if I can answer without making a hash of things. See thread below.
1. For CAP, we're considering only one object. In that case, serializability is a weaker property than linearizability (Not 'real-time').
2. 'Strict serializability', for one object, is the same as linearizability.
3. As Peter's page says, serializability generalises to more than one object in a transaction. Linearizability doesn't.
4. (The reason for that is that linearizability has other interesting properties which are lost for multi-object transactions).
5. (See cs.brown.edu/~mph/HerlihyW9…, section 3.3)
6. Yes, atomic consistency is the same as linearizability. See citeseerx.ist.psu.edu/viewdoc/downlo… (which is a paper you might read!), section 2.1.
