You're talking of Windows 10, going back to Windows 7, and now you want to try upgrading to Windows 10 again. Worth a try, but I doubt if it's the solution.
Since you don't tell how the screen behaves in the BIOS setup, Windows Safe Mode and Linux, nor how it behaves if you go back to factory conditions, it's rather impossible to say if it's a hardware issue or a software issue. That's up to you to find out by trying all those things, which you seem reluctant to do.
About your last question: it's quite unlikely that a Microsoft download comes with more or better Lenovo stuff than you can get yourself from the Lenovo site.
Finally, to boot into safe mode repeatedly press F8 around the time the BIOS has done its job booting the laptop. Then it starts Windows and that, before booting in normal mode and showing the Windows screen, will go into that menu to ask you if you want anything else than a normal boot. That's standard Windows.