How can I add an existing field ("Send notification" field) to Quick create view in Calendar module?
In other modules you can add it editing a field:

But on Calendar module you can't edit any field.
@MacarenaReina try to choose Events in picklist:
In the Calendar module the possibility of editing is very limited.
Most basic changes require editing in the code, among others here https://github.com/YetiForceCompany/YetiForceCRM/tree/developer/modules/Calendar
try this:
in the table DataBase 'vtiger_field'
filter where the column 'tablename' = 'vtiger_activity'
change the column 'quickcreate' to 0 for activate
and change order of fields with 'quickcreatesequence'
Most helpful comment
try this:
in the table DataBase 'vtiger_field'
filter where the column 'tablename' = 'vtiger_activity'
change the column 'quickcreate' to 0 for activate
and change order of fields with 'quickcreatesequence'