Questions about Windows 10 Pro

Correct - provided that the 10 Home is also 64-bit.

I firmly believe that the predefined process was not followed (support.microsoft.com/en-us/windows/upgrade-windows-10-home-...). The initial key may not have been a "real key" but a fake key. Another option is to do a complete reinstallation with W10 Home and then upgrade, or much easier to use a full OEM version that is not much more expensive.

at Lizengo.ch you can get the key for a third of the price.