Is there any way to prevent deletion of certain files from user owned directory?

Make the file immutable with the i attribute.

chattr +i file.desktop

see man chattr for more information.

(I dislike intruding users' home, I think they should be allowed to do whatever they want to do with they homes… but anyway…)

This should work on linux (at least). I'm assuming user is already a member of the group user. A solution is to change ownership of Directory1 and set the sticky bit on the directory:

chown root:user Directory1
chmod 1775 Directory1

Then use:

chown root Directory1/CantBeDeletedFile

Now, user won't be able to remove this file due to the sticky bit¹. The user is still able to add/remove their own files in Directory1. But notice that they won't be able to delete Directory1 because it will never be emptied.

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^{1. When the sticky bit is enabled on a directory, users (other than the owner) can only remove their own files inside a directory. This is used on directories like /tmp whose permissions are 1777=rwxrwxrwt.}

I don't think there is a way to prevent deletion of an individual file with Unix file permissions, but I can think of a workaround: write a daemon that replaces it when it is removed. inotify-tools is perfect for this sort of thing if you're on Linux.

There are a few ways you can replace the deleted item: copy a new one in place, or keep the real file in a safe place and just copy a link into the user's directory. For the link, you can either use a symlink or a hard link. I'd start with a symlink, but some (very few) programs don't handle symlinks correctly. If you find that the user encounters a program like this, use a hard link instead.