What are possible reasons, that i cant make directory? I noticed that using "dir" command, i see i have 0 bytes left on Z "drive". Why can this happen?

Your Z drive in dosbox is not a real drive. It is only a virtual drive.

Before you can do something you should mount a directory in Dosbox with the mount command. the first argument for this command is the drive letter and the second argument the directory you wan to mount.
for example
mount c c:\mydosboxdrive
where c:\mydosboxdrive is a directory on your real harddrive in windows.

Now you can go to your new drive and create a directory there