It was pointed out to me that my server is insecure, because anyone could read any file through PHP, even if it was out of his DocumentRoot.
I decided to reconfigure whole apache and all configuration files for virtual hosts and installed Mod FastCGI and I managed to get it running quite nicely, I don't have problems with rights anymore.
But there seems to be another problem. When I try to load more than 3 sites (on different VirtualHosts => different users on different threads) page loads for a while and than crashes on "Error 503: Service Temporarily Unavailable".
I tried increasing PHP_FCGI_CHILDREN var from my default setting for all VirtualHosts which is 0 to higher numbers, but without luck. I also tried to set KeepAlive var in my apache2.conf to Off as I read in some tutorial, but it seems like nothing helps.
Does anyone know how to resolve this issue? [My Apache error.log and suexec.log is empty.]
Found the answer to my own question. There are few more settings I overlooked.
FcgidMaxProcesses 15
FcgidFixPathinfo 1
FcgidProcessLifeTime 0
FcgidTimeScore 3
FcgidZombieScanInterval 10
FcgidMaxRequestsPerProcess 0
FcgidMaxRequestLen 33554432
FcgidIOTimeout 60
Those are my settings in apache.conf and everythings works as expected.