How to enable PMI (Performance Monitoring Infrastructure) Data Collection and what is the use of "PMI" in WebSphere Application Server?
What is a "Core Group" WebSphere Application Server?
What is the difference between JSESSION ID and CLONE ID in WebSphere Application Server?
To enable PMI Data Collection you should go through the WebSphere Documentation.
The JSESSIONID is a standard cookie used by servlet containers to identify your current session (it's the Session ID). WebSphere, when working in a clustered environment, uses a special value for that cookie which includes the Session ID, a Cache ID and a Clone/Partition ID. The last one from that list identifies the specific WebSphere server instance inside the cluster.
Regarding Core Groups:
A core group is a high availability domain that consists of a set of processes in the same cell that can directly establish high availability relationships. Highly available components can only fail over to another process in the same core group and replication can occur only between members of the same core group.
More info about them in the docs.