The key question is "how are you adding the new record?"
Example: IF you have a layout based on Christmas Ballet Act I Licensing Info with a portal to License Status Summary. If you enter data in the bottom blank row of this portal, then yes, FileMaker should automatically enter the Title, performer, Master Licnese Status and Sync. License Status fields from Christmas Ballet Act I Licensing Info into this new record.
If you just go to a layout based on License Status summary and create a new record, then no, the data from Christmas Ballet Act I Licensing Info will not be automatically entered. You would need to set up a method for entering this information. Scripts can do this and you can also set up these fields with drop down lists or pop up menus for selecting the needed values to match the new record correctly.
Note: I think you should take a step back and rethink your entire design. You appear to be creating very specific table occurrences (the boxes in your relationship graph) and long, detailed lists of match fields that are unlikely to match to more then one record in the related table. With your current approach, it would seem you would need a new layout (and new table occurrences) for each new Ballet act. Such an approach is very laborious and there alternatives that make this unecessary. (You can, for example, create a single layout for all Ballet acts and use finds to pull up all records for a specified act to see and work with all records for a given performance (or part of a performance).