If I encrypt a flash drive using BitLocker on a Windows 10 Pro (With BitLocker supported and installed) device and put it in compatible mode, can I enter the key and read/write to and to/from it from a Windows 10 Home device (without BitLocker supported or installed)?
Yes, you can unlock and use the device even on Windows 10 Home edition. However, you won't be able to manage the BitLocker.
Also, BitLocker is a part of Windows and is installed on every Windows copy by default.
Whether is it in compatible mode or not is not important in this case (Home/Pro). That would be important if you use older versions of Windows 10 or even older versions of Windows (8.1, 7, ...)