Aura Professional allows up to 256 GB storage currently. You can contact us to ask for more info about scaling with Aura Enterprise.
Self-hosting you are correct your own hardware would be the limitation. You may need to enable the High Limit format though to deal with the number of elements:
Note: Standard is the default in Enterprise and the only format available in Community. It has a limit of 34B nodes, 34B relationships, 68B properties.
High Limit is only available in Enterprise and supports virtually unlimited numbers of nodes, relationships and properties.
CAP is more about registers than databases, but to approximate, in a causal cluster we favor CP over A.
Causal clusters provide causal consistency (for reads, when using bookmarks explicitly or when executing queries within the same session) or eventual consistency (when not using bookmarks, a follower or read replica may not yet be caught up with the latest transactions). Queries directed to the leader or a single standalone instance always have read-committed consistency.
Ignoring Fabric for the moment and just looking at a causal cluster, the Raft algorithm used by causal clustering grants us resiliency in the face of network partitions and grants us some degree of availability in the formula of M = 2F + 1 where M is the number of Core Servers required to tolerate F faults. Or, put more simply, we perform quorum commits, and quorum is required for both leader elections, and to keep write capability.
If we lose quorum, then the cluster sacrifices (write) availability, and falls into a read-only mode in order to preserve consistency until quorum is restored. As long as quorum is retained, we can suffer core failures and still offer write availability.