Explanation
The Assignment Rule checkbox is a checkbox that appears on manual case creation pages when assignment rules are defined for cases. The Assignment Rule checkbox determines whether or not to apply assignment rules to manually created cases. If the Assignment Rule checkbox is selected by default, then any manually created cases will be assigned according to assignment rules instead of being owned by the agent creating them. To prevent this from happening, an administrator can either deselect the Assignment Rule checkbox when creating cases manually; or change the default setting for this checkbox under setup by selecting or deselecting Use active assignment rules by default. References:
https://help.salesforce.com/s/articleView?id=sf.customize_casesupport_assign.htm&type=5

There are two possible reasons why users are unable to access a report based on a custom report type created by an administrator. One is that the custom report type is in development mode, which means that it is not deployed and available for use by other users except for administrators and users with manage custom report types permission. The other is that the report is saved in a private folder, which means that it is visible only to its owner and not shared with other users or groups. References:
https://help.salesforce.com/s/articleView?id=sf.reports_builder_custom_report_types.htm&type=5
https://help.salesforce.com/s/articleView?id=sf.reports_builder_folders.htm&type=5

Case escalation rules are a way to automatically escalate cases that meet certain criteria, such as being open for more than a specified time or having a certain priority. Escalation rules can assign cases to a different owner or queue and send email notifications to the support manager or other recipients.References:https://help.
salesforce.com/s/articleView?id=sf.case_escalation.htm&type=5