1. Local script filename (and location) which needs the outbound connection:
Your store's /index.php is the script that initiates the communication, with the involvement of several other .php files.

2. Remote server IP address and port number:
IP Address as stated in the error message.
Port is 443, since it's operating in SSL mode.

3. Exact purpose of this connection:
Processing payment transactions for online store through payment gateway.