It is safe to disassemble a HDD if you want to try to fix it, but you will likely be unsuccessful without a lot of experience as Tetsujin suggests. You can readily find tutorials with the search phrase "HDD platter swap", there's even a wikiHow on the topic.
HOWEVER, you are presenting more than just one issue here. It may not be just the hard drive. "I tried to install Windows 10 on that drive, but it wouldn't recognize the USB drive." This could be a simple procedural error (not setting the thing to boot from USB, not having the drivers for the system hardware, etc.) or it could be indicative of further damages to the Laptop.
I treat my technology like my bank accounts, but sometimes I need the accountant to look over my books. Time to let a repair guy take a look?