I'd say these are false positives also, the remaining ones. Reason being, one has to give their root password, to allow any infection to run. While it's not impossible for someone to write a script & do this remotely on Linux, it's a lot of trouble. One would have to be really out to get you, at all costs, to pull this off. Plus it would be quite expensive to do so, to pull a prank.
Laptop still works but start-up is a little different than before, the little swirling icon does not come up as it did before right away.
Swirling icon on Linux Mint? These, I've only seen on Windows, and know that you dual boot with XP (or that XP is installed, don't know how often, or if, you run the OS).
If this is on XP. you may want to post in the "Am I Infected" section of the Security forum (after running a Full scan with your security, after updating). Did you click onto the same bad link on that OS, as you did on MInt?
Whatever link it is, you need to delete from all of your OS's, before you do anything else.
Also, hard shutdowns are hard on most any OS. It's best to use the keyboard combo (Ctrl+Alt+Delete) to gain Task Manager Access (Power down options on Linux MInt). From there, one of the tabs (I believe "Power" on Windows) has Restart & Shutdown tabs to safely shutdown or restart. If the keyboard combo doesn't work, on either OS, you have problems to address ASAP.
By trying this out to check for you (on Linux MInt), I inadvertently hit Shutdown, rather than Cancel, fortunately most of this post was auto saved.
So either print this, or write down these instructions for future use, as you don't want too many hard shutdowns, at best, this can cause file corruption, at worse, hardware failures, the system isn't designed for this. It's kind of like with a desktop PC, yanking the power cord from the wall socket. The computer requires proper shutdown. Only in a very serious emergency you want to force a shutdown, like if there's an odd sound or burning smell coming from the computer.
You may wish to boot into your other OS, update your security & run a Full scan with whatever security software is installed (as noted above).
Good Luck with this.