Explanation
A quick action is used to create a record from another record with predefined field values. By defining a quick action to create a work order from a case, the agent can easily create a work order for on-site support after verifying the customer's entitlement and product.
References: https://help.salesforce.com/s/articleView?id=sf.fsl_quick_actions.htm&type=5

Explanation
Changing the Work Order with a closed status of "Cancelled" allows tracking Work Order cancellations and subsequent follow-ups using reports or dashboards based on Work Order status field values[23. Re-using the existing Work Order for the follow-up allows maintaining the relationship between the original customer request and the follow-up action without creating duplicate records[24. Changing the Work Order with a status of "New" would not indicate that it was cancelled before. Creating a child Work Order for the follow-up Work Order would create an unnecessary hierarchy of Work Orders that could complicate reporting and scheduling.
References: [23. https://help.salesforce.com/s/articleView?id=sf.fs_work_orders.htm&type=5 [24.
https://trailhead.salesforce.com/en/content/learn/modules/field-service-lightning-basics/field-service-lightning-w

This option allows tracking the time spent on each step of the work order line item and associating it with the time sheet entry record. References:
https://help.salesforce.com/s/articleView?id=sf.fs_time_sheets_overview.htm&type=5

Explanation
Multi-day service appointments are used when jobs can take longer than the available resources hours in a day or require consecutive days of work and can span over weekends. Jobs that need to be performed at the same site on the same day of the week or require multiple stages of work performed by different resources can be handled by single-day service appointments with appropriate scheduling policies and optimization rules.
References:
https://help.salesforce.com/s/articleView?id=sf.fs_multiday_service_appointments_overview.htm&type=5

Explanation
Custom gantt filters are filters that allow dispatchers to view service appointments based on specific criteria such as status, priority, or custom fields[67]. Creating a custom gantt filter would allow providing a view of emergency work that is only visible to dispatchers by setting up criteria such as status equals emergency and sharing the filter with dispatchers only[68]. Custom lightning component is a component that allows developers to create custom user interfaces using Lightning Web Components or Aura Components[69].
Creating a custom lightning component would require coding and would not leverage the existing gantt chart functionality. Custom report in a private report folder is a report that allows users to view data based on specific criteria such as objects, fields, filters, or charts[70]. Creating a custom report in a private report folder would not provide a view of emergency work on the gantt chart and would not allow dispatchers to schedule or reschedule service appointments. Custom list view is a list view that allows users to view records based on specific criteria such as filters, fields, or sorting[71]. Creating a custom list view would not provide a view of emergency work on the gantt chart and would not allow dispatchers to schedule or reschedule service appointments. References: https://help.salesforce.com/s/articleView?id=sf.fs_gantt_filters.htm&type=5
https://help.salesforce.com/s/articleView?id=sf.fs_gantt_filters_create.htm&type=5
https://developer.salesforce.com/docs/component-library/documentation/en/lwc
https://help.salesforce.com/s/articleView?id=sf.reports_builder_overview.htm&type=5
https://help.salesforce.com/s/articleView?id=sf.customize_listviews.htm&type=5