You can easily do a "snap to grid", or "keep position" (something looking like that) with a right-click on each icon, but nothing can be done to prevent accidental removing. On the other hand, it is very easy to add them again, just go to the menu entry from the general menu button, right-click on the desired entry and select "add to desktop".
I have put all these icons on the desktop to easy their finding, because the menu entries can't be tweaked easily to get a section specific to Edu games, directly available as main menu, or first sub-menu... but you will always find them in the general menus anyhow, if you search a little. You can also find a copy of them all, in the directory : /etc/skel/Desktop.
Thank you for sharing your joy to have it. I am happy to know you are one more user who likes it and finds it useful.