I think the first thing that should be cleared up is what do you mean by 'client' and 'server'
'Server' always refers to the Exchange Server itself. If the Mailbox Archiver agent is installed on the server, then the 'Server' can also refer to the client which performs the archive
'Proxy' refers to an off-host client (other than the Exchange Server) where the Mailbox Archiver is installed to perform Archive operations in cases where the agent is not installed on the Exchange server itself
'Client' - honestly this could mean anything, as all machines are clients. In my description I would typically differentiate clients based on 'Server', 'Proxy' or 'Outlook Client' where:
'Outlook Client' refers to the end user's workstation where the Outlook Add-In is installed.
our 'Offline Archive' process has two parts
1) on the 'Server' or 'Proxy' where the archiver agent is installed, we run the Archive job for Mailbox Archiver agent with the 'Offline Archive' option enabled. In this phase the message data is sent to the media agent to be protected on the back end. In the stubbing phase for this job, the messages are not stubbed on the Exchange server, the only change is the message class is changed which will change the message icon to the 'G' icon. Emphasis on the fact that the original message is still on the Exchange server at this time!
2) phase two happens on the Outlook Add-In client on the end user's workstation. an Offline Archive job is run from Outlook which will stub the messages by moving the originals into the cvpst file and replace them with the stubbed file. If Outlook is in online mode, stubbing will happen directly on the Exchange server so it is synced immidiately. If Outlook is in cache mode, the stubbing will happen on the .OST file which will then by synced back to the Exchange Server when it is connected. if Outlook is in cache mode, but also has connectivity to Exchange this will all happen in the same process.
Now lets see if we can answer your questions
1) I think i answered this in my previous paragraph. is the answer sufficient?
2) if Offline Archiving is selected in subclient properties, space is not reclaimed on the mailbox until the Offline Archiving phase is run on the end-user workstation from Outlook Add-In. Optionally, there is one exception to this rule and that is when the following key is configured for Mailbox Archiver agent http://documentation.commvault.com/commvault/release_9_0_0/books_online_1/english_us/features/registry_keys/registry_keys.htm#nOfflineArchivingTimeout
Feel free to comment or ask any further questions you have on this process
Wearer of Many Hats