You are asking allot of generic questions which you can lookup online and some depend on versions of outlook and Exchange.
1. Deleting mailboxes from a database will NEVER reduce the physical size of an EDB. First the deleted mailboxes need to pass the retention date which by defaults is 30 days. Once that is done you can run eseutil /d to reclaim the space, however
that takes all mailboxes within the DB offline for a long time. Better action is to create a new EDB and migrate users from old to new DB and when completed remove the existing EDB
2. Other items you can figure out with a google search like this
http://lmgtfy.com/?q=Protocol+used+by+lync+to+initiate+a+session
Search, Recover, Export Mailboxes, Folders, Email, Contacts, Calendars, Tasks, etc. from Offline Exchange Databases (EDBs), On-Premise Exchange Servers and Office 365. Migrate/Recover direct from any offline EDB into any On-Premises Exchange Server, even
cross version i.e. 2003 → 2007 → 2010 →2013 → 2016 → Office 365 with
Lucid8's DigiScope