http://answers.microsoft.com/en-us/windows/forum/windows_7-update/windows-update-error-8007001f-when-upgrading-to/e3a8a757-fd4a-4dcf-b2aa-10749cd2073e?auth=1 blames grub. Can that be the case?
http://appuals.com/best-fix-steps-fix-update-error-c1900107/ is the first google hit for the second error.
You might find more googling these error codes yourself.

If update via Windows update fails, try it via USB or DVD (donwload the iso-file and use the Windows Media Creator).

If that fails also, wait till the next release when you can do a clean install of Windows 10 with your Windows 7 or Windows 8.1 license. Or buy that Windows 10 license for a clean install right now, if you really feel you need it now.

An alternative might be to go back to factory conditions with Windows 7 or 8, do the necessary updates and then install Windows 10. Any interference from whatever causes the problem now should be gone.

Kees