It has to be in below format for logical operations AND and OR
Column 1 - 15
Column 2 - 9
Column 3 - 8
=AND([Column1]>[Column2], [Column1]<[Column3]) - Is 15 greater than 9 and less than 8?
=IF(AND([Column1]>[Column2], [Column1]<[Column3]), "OK", "Not OK") - If 15 is greater than 9 and less than 8, return "OK".
I think you are using Forms library not Document library (as you have the xml files in the library). If xml file in library is blank there is something wrong with the item (and InfoPath services will not be able to do with it anything). Issues may differ from problems during saving to data corruption on the DB side. If the latter you can try restore item ...
You could add a multiple-person column to store the users who attend the class in this calendar list. So the managers could add the new hires to this column by editing the events.
To add a multiple-person column: click create column, choose "person or group" type and Allow multiple selections.
It sounds like you need to add a new list item content type to the Calendar list with a Multi-Line Text field called "Roster" and set it to append. Then the manager can edit the calendar event and add information into the roster field. If the new hires are already in your AD then you could make the Roster field a people field and allow multiple entries.