There is no single answer to this question, because some of these parameters can only be accessed in one way, some in other way, and some by multiple ways. It's bit messy, but the EasyAEClient just mimics the IOC specification, and cannot provide information where there is none, unfortunately.
In general, the AEConditionState can be obtained by calling EasyAEClient.GetConditionState only. You need to be aware that you get a snapshot of the state at the moment you are calling it, and that can already be different from the state it was in when you received the notification that triggered you to ask for the state. Sad, but true.
Therefore the only always reliable approach is to use whatever information you received in the notification itself. Here again, we give you everything that the OPC spec allows and the server provides. Some server may have vendor-specific event attributes which can convey the information. But, if something is missing, there is no way to reliably obtain it later. Some of what you have asked for can be easily inferred: For example, the time when a condition was acknowledged, is the time of the event notification when the condition state (which is included in the notification) has transitioned into the Acknowledged state. But the AcknowledgerId, for example, is not available in event notifications and, to my knowledge, can only be obtained through GetConditionState.