1. Is there a way to see a log of activity ?  I would like to be sure, when using real-time backup of a working folder, that modified files have been backed up.

You can not see the log file activity. However it is possible to check backup tasks by using DriveHQ FileManager. DriveHQ Online Backup also has a feature to automatically send emails notifying task status.

2.  When using real-time backup, are multiple versions of backed up files saved ?  I do not see how to examine anything other than the current version.

When using DriveHQ Online Backup to create/edit a backup task, you can setup the number of max versions to keep. So whether it is a real-time or scheduled backup, it can keep multiple version files.

To restore an old version, using DriveHQ Online Backup, click on the Restore tab, then highlight a file and click on History in the popup menu.