MSI Templates that are saved locally in SFDC under My Templates would be saved in SFDC.
If you have the correct settings, each send is logged to the SFDC Activity History in full.
You cannot review all users easily. As an SFDC Admin, you may be able to view all of the email templates. Not sure how though.
For your second question, what do you mean about Lead Partitions? Unless your SFDC also uses Partitions (Divisions?) that match Marketo, there are no restrictions for MSI in this way. Now, if an email asset and lead exist only in the Asia partition, then it is less likely you'd get a salesperson looking at the NA version of MSI email. But it is POSSIBLE for a salesperson to see the entire tree of MSI emails in the drop down. But I'm not entirely sure if the lead would be allowed to get an email not within her partition in Marketo. Verify in Docs.marketo.com or let's ask Support.