3) I tried mounting: md c:\test\offline and using it as a source(also using install.esd and install.esd), but DISM simply ignores me.
This sequence worked on my Win10 test VM. I should note that my VM was not "broken".
Mount the Windows iso that matches your OS version. Use the drive letter (I have F:) and desired folder name in the following commands.
Find index of Win version
dism /Get-WimInfo /WimFile:F:\sources\install.esd
Export the wim file using the correct index. (6 was win10 pro for me)
dism /export-image /SourceImageFile:F:\sources\install.esd /SourceIndex:6 /DestinationImageFile:c:\temp\install.wim /Compress:max /CheckIntegrity
Double check that the wim matches your OS.
dism /Get-WimInfo /WimFile:c:\temp\install.wim
Run the repair.
Dism.exe /Online /Cleanup-Image /restoreHealth /source:c:\temp\install.wim
A reboot would likely be the next step followed by another run of IsWindowsHealty.bat.
If that doesn't fix your OS then you will probably need to reinstall the OS.
This site suggests that you can do an inplace upgrade. I have no idea if that will work or not. I didn't try it.
https://www.techspot.com/guides/1764-windows-repair-keep-all-your-files-intact/
You might have to do a reset.