Yes, most modern-day controls systems can integrate with a third-party system, dependent on the type of system that is to be integrated with, you can communicate via protocols such as BACnet, Modbus or Mbus.

Most control systems have the ability to have firewall protection. But it is common to have the control system on a separate IP network from the main building IP network system. This is because the controls would have no internet connection, this is so that no outside entity can infiltrate the control system's network. If the system is to use the buildings network infrastructure, by protocol, the IT department would ensure that the system is secure from outside connection using their own firewall.

There are many control systems out there, and most are quite similar in what they do. But some do have better integration protocols, and some have better remote connection availability, but it all depends on they type of plant that is being controlled and how much information is required.

With the introduction of Trend Controls IQVision and Tridium's Niagra AX, these are graphics packages that can negotiate with most control systems as they use the BACnet integration protocol. This allows the graphics software to pull information via the BACnet gateway from the third party, to display operation, temperatures etc...

Most control systems have the ability to send alarms via a router to a remote connection such as text message stating the alarm. They can also be sent via email using the IP network through a router to a designated email stating an alarm. The remote alarm system normally sends critical alarms such as Fire and Critical plant failures, for example,  that look after IT comms rooms etc...