Explanation
The command that lists firewall chain is fw ctl chain1. This command displays the list of chain modules that are registered on the Security Gateway2. Chain modules are components of the Firewall kernel that inspect and process packets according to the security policy and other features3. The order of the chain modules determines the order of the packet inspection and processing3. The fw ctl chain command can help you troubleshoot connectivity or performance issues, or to verify that a feature is enabled or disabled on the Security Gateway2. To run this command, you need to access the Security Gateway in expert mode and run fw ctl chain1.
References: How to use fw ctl chain - Check Point Software, fw ctl chain - Check Point Software, R81.x Security Gateway Architecture (Logical Packet Flow) - Check Point CheckMates

The type of Endpoint Identity Agent that includes packet tagging and computer authentication is Full. Packet tagging is a feature that allows the Endpoint Identity Agent to add a tag to the packets sent by the user's device, which contains the user's identity information. This way, the Security Gateway can identify the user without requiring additional authentication methods. Computer authentication is a feature that allows the Endpoint Identity Agent to authenticate the user's device using a certificate, which ensures that only authorized devices can access the network resources. The Full Endpoint Identity Agent supports both packet tagging and computer authentication, as well as other features such as Single Sign-On (SSO), Multi-Factor Authentication (MFA), and VPN.
The references are:
Check Point R81 Identity Awareness Administration Guide, page 15
Endpoint Identity Agent - Check Point CheckMates
Check Point Identity Agent - All flavors for Windows OS in a single package (Full, Light, v1 and v2 for Terminal Server)

https://sc1.checkpoint.com/documents/R80.30/WebAdminGuides/EN/CP_R80.30_Multi-DomainSecurityManagement_AdminGuide/124911.htm

The API server is a service that runs on the Security Management Server and enables external applications to communicate with the Check Point management database using REST APIs. You can verify that the API server is responding by using the following command in Expert mode:

This command will display the current status of the API server, such as running, stopped, or initializing. It will also show the API version, port number, and SSL certificate information. Reference: Check Point R81 REST API Reference Guide