Bottom line: you have none.
Go look at the posts and comments on this by potnia theron and fighty squirrel. If you use your University's network access, you may as well consider them to have a list of every site you visit, if not a keylogger for what you do online. If you use your business email address for non-business things, you are inviting your boss to know anything you wrote. When I worked at National Lab, we knew our phones and mail accounts were monitored, so people used cell phones/alternate email accounts or face to face meetings for private discussion. What is true then is as true now--never, ever put anything in email that you would not mind becoming public knowledge. If you get involved in anything that triggers an investigation of you (even as a witness to something, even if it was something crazy your office mate did, even if it is something innocuous taken out of context), your electronic history will be combed through in detail. Best to confine specific gripes about specific people to in person conversations!
At the same time, while privacy tools like TOR help, human nature is working against you. It is really, really hard to stay anonymous on the Internet. One minor mistake posting using the wrong account, checking email without TOR, or referring to something done by an alternate persona, and you are done. Private VPN sites don't work for everything one might want to do, making it really hard to stop your access provider from tracking you at least some of the time.
I use a thin pseud because I don't want it to be easy to find me, but I am well aware that there probably are people who know (or could find out quickly if they so desired) who I am. Almost everyone in truth relies on "I am a tiny needle in a giant haystack" for privacy, but that only works if no one decides to look for information about you.