1. If a client goes offline how will SEP handle this? Will it remove the client from its list after a certain amount of time (please tell us how long) or will it wait for the active directory to be updated?
Ans: Integration with AD when you will delete on Actve Directory Automatic Delete ON SEPM console.
Without Integration with AD.You can set Specify Dates.
Duplicate SEP clients appear in the Symantec Endpoint Protection Manager console
https://www-secure.symantec.com/connect/articles/duplicate-sep-clients-appear-symantec-endpoint-protection-manager-console
2) If a client has no agent will it appear in SEP if I searched for it? Because we can see some clients that are one SEP but they don’t have an agent installed on them
Answer:How to repair duplicate IDs on cloned Symantec Endpoint Protection 12.1 clients
http://www.symantec.com/business/support/index?page=content&id=TECH163349
3.) There are some clients which they have an agent installed on them yet they don’t appear in SEP. Could you tell us what is most likely causing this?
Answer :I think you are using Image OS.