Does Forced shutdown damage Mac? Does Forced Shutdown, pushing power button until Mac shuts down, damage hard drive? Or operation system?

Can it cause damage to Mac's security so it will get weaker towards malicious things?

And if I run Disk Utility after forced shutdown, will it find any potential damage?

I've had it happen few times, but no underlying continuous problems, just want to know what could happen.
A forced shutdown doesn't damage your hardware nor does it weaken your security.

What it could potentially do is corrupt files because you are turning off the computer while they are open/active.  These files can be anything from an open webpage or text file to system files that in use for any reason (like an update).

fsck checks for inconsistencies in the filesystem.  Meaning it looks at the blocks, the inodes, the used space, the free space, etc. to see if everything "adds up."    For instance, it will check the blocks and the sizes, if there is an error it will attempt to fix.

However, it won't repair a file that has been corrupted or the data lost - it simply can't recreate data.

As for "being dangerous to security" there's no direct link to your filesystem getting corrupted and security being compromised.  If your file system has been corrupted to the point that services fail to load or critical files cannot be loaded you will know about it as the system will generate errors.

It will NOT suddenly open ports in your firewall or make your password go blank.