Hello

I wonder... lets say I have to set up very very restricted rights to a user that only should be able to access logfile Y in catalogue X and nothing else. Current user is going to use Putty to access current unix machine.

Is it possible to set up user settings so a user is just able to access its HOME directory and being able to "tail" and/or "grep <word>" for logfile Y. The logfile Y is not in current users HOME directory and its important that current user is not able to execute other commands than thoose beeing mentioned and is not able to change catalogue. If answer is yes how do I do that.

You can chroot a user - you make his home directory root - then create the user's own custom /usr/bin directory with only the commands (plus the shell) that you want the user to have.

try reading this:
Best Practices for UNIX chroot() Operations