I want to make a widget but it should be uninstallable or undeletable from home screen (if possible) like "google search" widget on nexus & moto phones. I searched it already but didn't find anything related to this. Is it really impossible to built such widgets?
Yes. The decision of what widgets to allow users to add and remove is up to the home screen implementation, not you. So, for example, if on "nexus & moto phones" you install a third-party home screen, the Google search widget may or may not be available at all, let alone non-removable.
If you want to force people to have certain things on their home screen, write a home screen, then use heavy weaponry to force people to use that home screen. Note that the use of heavy weaponry may be illegal in some jurisdictions.