Can I publish a source code containing potential copyright violations that someone gave me at a university (updated)?

With the caveat that I am not a lawyer, the answer is "no".

You have:

• code A, which is GPL-licensed
• code B, which is a derivative work of A and not GPL-licensed.

The GPL license requires that all derivative works are also GPL-licensed. As B does not carry the GPL license, it is a copyright violation and (depending on jurisdiction) it is probably illegal for you to distribute it.

If the changes needed are small, your simplest way forward would be to take code A, and modify it yourself as needed to make code C, while keeping it GPL-licensed, and release that.

EDIT: As noted in the comments, it is possible that A had two licenses: The GPL, and another license granted specifically to the author of B which permitted them to change the names and redistribute without GPL. This seems very unlikely, but you should consider the possibility if considering accusations of any sort.

What that person did, was not just plagiarism, but also copyright infringement. They took a GPL licensed work (legal), modified it (still legal), published it, but not under the GPL license (copyright infringement), and claimed it as their own work (plagiarism).

If you wanted to be nasty, you could tell the original author of the code about this, and if that person decides to sue for copyright infringement, that university and everyone involved is in deep trouble. I would be curious to know whether anyone ever managed to get their thesis revoked, not for plagiarism, but for copyright infringement plus plagiarism.

No, you are absolutely not allowed to use this software in any way, shape or form, unless you get the permission of the copyright holder. Or if the person producing the modified code gives you another copy including the GPL license.

I cannot understand how a university would have allowed this. Quoting some text without reference is bad enough, but actively removing copyright notices, license information, and author names, that's an entirely different level.