For me this was also a problem with the PATH-variable.
Go to environmental variables, search for PATH and add at the end: ;C:\Windows\system32. The semicolon is important as it separates the entries.
You can test it by typing cmd into the console. If it works (and you had the same problem like me), tlmgr may now update properly.
Restart the console after changing environmental variables.
Thanks a lot. That was my problem, too. I added ";C:\Windows\system32" at the end of the PATH environmental variable - and the installation worked out fine. You amde my day! :-)
Yes, it is default behaviour of MiKTeX to install missing packages “on-the-fly”, but this can be changed in the Options dialogue. All in this way installed packages go into %APPDATA%\MiKTeX\<version>\ (<version> is 2.9 at time of writing), the MiKTeX variable is UserInstall. Since Windows Vista %APPDATA% resolves to C:\Users\<username>\AppData\Roaming, therefore your observation.
But this needs an active connection and a responding download mirror. At least one of these two things did not work in your case. If it was the mirror you can take a look on the CTAN mirror monitor Status of CTAN Mirrors, and if necessary in MiKTeX settings change the active mirror (MiKTeX Options, in tab “Packages” the first line shows the active MiKTeX repository and on the right you can change it).
I prefer to install all packages with the Package Manager, but this needs to be done on a regular basis, about once a week, and of course one needs enough disk space. In the rare cases, when I was asked for installation, I stopped this and ran the installation with the package manager. (Note, that this is different from, what is usually meant with “manual installation”! You already linked to the according question.)
All with the package manager installed packages go into the main MiKTeX tree (see Root 3 in your question), if you made the update in admin mode or in single user installation with writing rights in this folder. If you did a user mode installation packages will always be installed in UserInstall.
One would expect, that installation in admin mode goes into CommonInstall, what is the same folder in your case. But on my system this is not used, the folder, to whome CommonInstall points, does not exist!
Other related questions, at least partially:
Best Answer
I recommend to install or to update the complete
pgfpackage.