Thank very much for your help. Now all typo3 - sites are working well and your advisings helped me to eliminate the errors.
After having done your changes, I found this forumarticle:
Configuring open_basedir to allow access to a script for all sites?
I think, while updating to the version 1.2.13 my configs in the parameter open_basedir would be overridden. And in fact, this follows to the raising errors. And in the actual control-panel I can't still find the field to set the value for open_basedir, globaly or by domain.
While using open_basedir I could save all typo3 sources in a directory outside the domains reached by vu20xx. This was usefall, because the same source-version had only to be saved once.
May be, there is a posibility to set an open_basedir value, which isn't touched throu i-mscp updates .
Have a good time