CAP consistency is linearizability, so if what you mean is there are other models of consistency available to "AP systems" (kind of hate the framing that these are binary features of a distributed system rather than a huge space of design choices, but anyways), then yes that's true. But AP systems don't always guarantee things like read-your-own-write consistency models, and not all conflicts that occur during a partition can be resolved in many of these databases.
Sure. But it's kind of is a huge space of design choices (https://jepsen.io/consistency), so it's not ok to claim you give up consistency with any of them.