Stateful Inspection is a firewall technology that inspects both the header and the payload of each packet and keeps track of the state and context of each connection. Packet Filtering is a firewall technology that inspects only the header of each packet and does not keep track of the state or context of each connection. A benefit that Stateful Inspection offers over Packet Filtering is that only one rule is required for each connection, whereas Packet Filtering requires two rules for each connection (one for each direction). Stateful Inspection also offers other benefits over Packet Filtering, such as enhanced security, performance, and flexibility. Stateful Inspection does not offer unlimited connections because of virtual memory usage, nor does it avoid using memory to record the protocol used by the connection. References: [Stateful Inspection], [Packet Filtering] , [Firewall Technologies]

Automatic Hide NAT rules are created by the administrator when they configure NAT for network objects or groups in the object properties. Automatic Hide NAT rules allow multiple private IP addresses to share a single public IP address when accessing external networks. Source Port Address Translation (PAT) is enabled by default for Automatic Hide NAT rules, which means that the Security Gateway assigns a unique source port number for each connection from the same source IP address. This allows the Security Gateway to keep track of the connections and translate the reply packets correctly. 

The pen-symbol in the left column means that the rules have been edited by the logged in administrator, but the policy has not been published yet. It indicates that the changes are not yet effective and can be discarded. References: Policy Editor, Publishing Changes