Errors 0x800B0100 and 9C59 when trying to install Windows Updates

You have rather a large number of errors there...

Code:

Summary:
Seconds executed: 1139
 Found 104 errors
  CSI Manifest All Zeros Total count: 92
  CBS MUM Corrupt Total count: 6
  CBS Catalog Corrupt Total count: 6

Luckily they all appear to be from the same update - KB3003057 - so shouldn't be too hard to fix.
I'll post a fix protocol later.

I've uploaded a file - lkfaa.zip - to my OneDrive at Noel's OneDrive
Please download and save it.
Right-click on the downloaded file, and select Extract all…
Extract to the default location - which will create a new folder lkfaa in the same place.
Open this folder - there should be two folders inside it (Manifests, and Packages)

Copy the content of the Packages folder to the folder
C:\Windows\Temp\CheckSur\Servicing\Packages

And the content of the manifests folder (.manifest files) into this folder:

C:\Windows\Temp\CheckSur\Winsxs\Manifests

Now run the CheckSUR tool again (it may take a while)

Post the new CheckSUR.log file, and the CheckSUR.persist.log file.

Great! CheckSUR is happy now
Do a Check for Updates, and attempt to install ONLY the oldest update found - if it goes in OK, try the rest.
If it fails, post the error message, and the new CBS.log file.

You're welcome - good luck!