Each .ics feed can contain info about the event in following fields:
- Event Title
- Event Description (optional field)
- Location
and dates of event, of course.

1) During import of .ics feed from external source into the Booking Calendar, you can assign each such specific field to one of exist fields in the booking form. You can make this assignment at the Booking > Settings > Sync > "General" page in "Import > Assign events fields to specific booking form field" section.

Please note, email field here is not required (but this field is required for the Booking Calendar). So that's why during import of events from .ics feed into the Booking Calendar created new email field and assigned your "Administrator email" from your WordPress website.

2) During export of events from the Booking Calendar into the .ics feed, Booking Calendar assign following values to standard .ics feeds fields: "Title" and "Description".

If you are using the Booking Calendar Free version, so then plugin export into "Title" field following fields (if fields with such names exist in your configuration at Booking > Settings > Form page): 'name' 'firstname' 'secondname' 'lastname'.

In paid versions of Booking Calendar, plugin export into "Title" field of specific event, - configured "Title" of booking that is showing in Calendar Overview (timeline) page in booking pipelines. This configuration you can find at the Booking > Settings General page in "Booking Admin Panel" section, in option "Booking title (admin panel)" - default title of bookings in calendar view mode at Booking Listing page.

As "Description" field, Booking Calendar export all booking data of specific booking. In paid versions of Booking Calendar its configuration of "Content of booking fields data" form from Booking > Settings > Form page.

If you need to remove any booking data (in "Title" and "Description" fields) in your exporting .ics feed, then you can activate this option "Remove booking details in exported .ics feed" at the Booking Manager plugin at menu "oPlugins Panel" > General Settings page. In this case, system will export only booked dates into the .ics feed without any additional details. this option available in Booking Manager update 2.0.12 or newer.

P.S. In case, if you need to make some your customization of such import / export process, so then you can find needed info for import in this file: ../wp-content/plugins/booking-manager/core/wpbc/wpbm-bc-import.php

function function wpbm_ics_import_start( $attr )

and for export in this file: ../wp-content/plugins/booking-manager/core/wpbc/wpbm-bc-export.php

function wpbm_export_ics_feed__wpbm_ics( $param = array( 'wh_booking_type' => '1', 'wh_trash' => '' ) ) { 

P.S.S. Disclaimer. Unfortunately we can not start, right now, some personal customization or custom development, because almost have no free time. Check more about new features here https://wpbookingcalendar.com/faq/need-new-feature/
Please note, if you will modify the source code of the Booking Calendar, we will not guaranteed the correct work of plugin and do not support it.