Yep, in Desktop Manager, the Sync application, there is a checkbox to automatically sync upon connection.
2. Yes, also, find that setting within Sync Configuration and uncheck Notify on Conflict, and decide if you want the Handheld or PC to have control of which data to control the sync.
There are options in Desktop Manager that should let you do both. You can set it to automatically sync whenever its connected. In DM go to Synchronize and there is a check box for automatically syncing.