To save a custom XQL query to the Widget Library, you need to click on "Save to Widget Library" in the dashboard and you will be prompted to give the query a name and description. This will allow you to reuse the query in other dashboards or reports. You cannot save a query to the Widget Library by clicking the three dots on the widget, as this will only give you options to edit, delete, or clone the widget. You also cannot save a query to the Action Center, as this is a different feature that allows you to create alerts or remediation actions based on the query results. You do not have to exit the dashboard and go into the Widget Library first to create a query, as you can do it directly from the dashboard. Reference:
Cortex XDR Pro Admin Guide: Save a Custom Query to the Widget Library
Cortex XDR Pro Admin Guide: Create a Dashboard

The Live Terminal feature in Cortex XDR allows you to initiate a remote connection to an endpoint and perform various actions such as running commands, uploading and downloading files, and terminating processes. You can disable the ability to use the Live Terminal feature in Cortex XDR by configuring the Agent Settings Profile. The Agent Settings Profile defines the behavior and functionality of the Cortex XDR agent on the endpoint. You can create different profiles for different groups of endpoints and assign them accordingly. To disable the Live Terminal feature, you need to uncheck the Enable Live Terminal option in the Agent Settings Profile and save the changes. This will prevent the Cortex XDR agent from accepting any Live Terminal requests from the Cortex XDR management console. Reference:
Live Terminal: This document explains how to use the Live Terminal feature to investigate and respond to security events on Windows endpoints.
Agent Settings Profile: This document describes how to create and manage Agent Settings Profiles to define the behavior and functionality of the Cortex XDR agent on the endpoint.

Local Analysis is a feature of Cortex XDR that allows the agent to evaluate files locally on the endpoint, without sending them to WildFire for analysis. Local Analysis is evoked when the following conditions are met:
The endpoint is disconnected from the internet or the Cortex XDR management console, and therefore cannot communicate with WildFire.
The verdict from WildFire is of a type unknown, meaning that WildFire has not yet analyzed the file or has not reached a conclusive verdict.
Local Analysis uses machine learning models to assess the behavior and characteristics of the file and assign it a verdict of either benign, malware, or grayware. If the verdict is malware or grayware, the agent will block the file from running and report it to the Cortex XDR management console. If the verdict is benign, the agent will allow the file to run and report it to the Cortex XDR management console. Reference:
Local Analysis
WildFire File Verdicts