Microsoft Office applications are unlikely to give them any of this kind of access. The most they would have is the ability to see the location and IP you sign into the app on, like if you visit London and sign into Microsoft Word there, they may be able to see that location and the IP you were given on the network there. Unless you got this from Microsoft who has built the app, then that’s a different story since they have much greater control over the software than your uni would.
The programs you most are worried about would be things like antivirus or VPN apps that have the ability and known history of tracking and logging events on the machine it’s connected to.
To determine the exact ports you’re using, such as in this app, one of the best ways I’m aware of is to have another deceive on the same network and have a program that listens/sniffs web traffic and then filter just for the device you are using to see what protocols are being used at a given time you’re aware. Time consuming and a bit of a learning curve to know what everything means and what you’re doing, but it works for this purpose.
As for your last reply about formatting the device…you can delete everything and this usually removes any spyware, but not always foolproof. In some rare cases, malware has been installed to the BIOS firmware, then no formatting of the Windows OS, for example, would fix this. Also, if something like Microsoft Intune was installed to the device, it’s possible that they can bring the computer back up from a restore or they have already backed up everything and can view it at their leisure. But in most cases, formatting is a good way to conceal yourself from prying eyes if you believe you may be compromised.