The Terminal app is normally located in the Utilities folder within the Applications folder ("/Applications/Utilities"). You can also use Spotlight to search for the Terminal app in case someone has moved it somewhere else. If the Terminal app has been deleted, then restore it from a backup or reinstall macOS over top of itself.
Are you including the leading slash "/" in the path? Your post here showing the path is missing the leading slash "/". The proper path is "/usr/local/bin".
The university network has nothing to do with the files & folders on your Mac unless you allow for remote access to your Mac.
If many things are wrong with the Mac system area, then try reinstalling macOS over top of itself which will restore all of the macOS system files. If that does not solve the problem, then you may need to perform a clean install by first erasing the drive before reinstalling macOS. Restoring or migrating from a backup is fine as long as you choose a backup made before all these problems started, otherwise you will just bring the problem back. If you don't have a backup, then you will need to create one (best to manually transfer your files to external media since macOS is already broken) and perform a clean install followed by manually transferring the files back).
TirNaNog_2001 wrote:
I can still move things to the bin, I just have no way to access it.
When referencing "bin" you need to be very specific about what you mean. If you mean one of the "bin" folders in the system area of macOS, then you really should be very specific and include the complete path. Are you still referencing "/usr/local/bin" or one of the other "/bin" folders on the Mac? FYI, users from other regions use "the bin" to mean "the Trash".
If you are using the command line you really need to be very careful describing things accurately here. Also using the command line requires a user to be very accurate on the commands & paths used since it is very easy to break macOS and destroy your data with just a slightest of a mistake. Always make sure to have a good backup before issuing any commands in the Terminal since even experienced users can make a catastrophic mistake.