Hello,

i have problems with the check patches installation:

* JFolder::create: The folder can´t create!
* Unable to create destination
* Error during installation of the file "administrator/includes/defines.php"
* Copy failed

* One or more backup file is missing. The original file(s) can not be restored.

Joomla Multi Sites version: 1.1.21
Patches definition version: 1.1.10

The permissions of files and folders are correct (777), on the server permissions of group and user of files are also correct. What can i do? Joomla version is 1.5.10.

You can try using the Joomla FTP Layer as explained in tutorial step 15.
This is only available for Unix platform.
On windows platform, see FAQ trouble shoting
www.jms2win.com/faq#sec-27

It don´t work with the Joomla FTP Layer. Could i patch the needed files manually?

This is almost impossible manually as you have to edit the files and peform the change in the original sources.

Only few files can be installed manually.

Try to find your permission problem.
I can tell you this is a permission problem that does not allow to create or update files and folders.

Perform a recursive chmod 777 on all files and folders but you say you already do that.

But the permissions shows ok (777 all files and folders) and owner/group of files and folders are also ok.

All depend on your platform.
If you are working on Windows platform, you have to change the permission differently.
See FAQ concerning the permission "everyone".

On Unix, sometime the only solution consist in using the FTP layer because the chmod 777 does not work.
See video in tutorial step 15 that show how to setup Joomla to use the FTP Layer.
The FTP layer will help you to bypass the permission use.