How does system start up affect backup for inSync client?

inSync client does not honor scheduled backup notification in initial 10 minutes. The idea is to reduce impact of backup on the startup process/applications. If server finds that the scheduled backup has not happened even after giving notification, it will again send a notification after 20 mins wait (or less if interval is less than 20).

Example:    
Client wakes up at 1:00.
Schedule backup is supposed to happen at 1:05, so server sends a notification. Client ignores it (as it will ignore all notification till 1:10)
Server sends another notification after 20 mins (i.e., 1:25). Client will honour this notification and the backup will start.

How does inSync client handle backup when a system log-off is executed?

If the log-off command is given, inSync client will first complete the backup and then log-off the user. Please note that MAPI (Outlook Files) or encrypted file backup might not work at logoff as USyncer exits on logoff.

How does inSync client handle backup during system shutdown?

inSync client does not hold off shutdown for backup to complete. Therefore, even if the backup is in progress, it may not complete depending on the time it takes to shutdown the system.

How does inSync client handle backup with the system is in sleep mode?

A backup would resume after the machine wakes up from sleep, provided the resources (like NIC interface) come up soon after the system is up and the previous connections do not get closed/invalidated. The default behaviour of inSync is to try to reconnect to the inSync Server and resume the backup. However, if the NIC interface is not restored or if there is a delay, then the backup fails. Therefore, the backup may or may not resume depending on the NIC interface connection and provided the previous session is not closed.