I created a page in Facebook where I now have to add some fans of the page to keep my page continuing. Now after making others admin, I can also see the option to "remove admin". So my question is can the newly made admins remove me i.e. creator of the page? Does this happen in case of "group", too?
Yes any Admin can remove or create new Admins. This is why you should only add people you trust as co-admins.