When you develop your code you should have all the error reportings in PHP enabled, including notices and warnings. Your production code should never produce a PHP Error. In some special cases you may survive with some PHP Warnings and Notices, but on your production server you should only show the Errors to the user.
Next, PHP Errors mean that you have something really messed up in your code and such things should never reach production. Any amount of decent automated tests will make sure this never happens. => Correction for clarity: "... will make sure this happens rarely."
I don't recommend you to transform PHP Errors, Warnings and Notices into Exceptions or "FALSE". Never! If they happen on your computer the application has a serious problem, so don't transform the error into something that you can catch and than forget / ignore easily.
When you have situations where your code can go wrong, use proper verification and throw exceptions. Even more, whenever possible make your own exception and throw the one most appropriate for that situation.
For example, instead of letting PHP throw an "Invalid index" when you try to read an element of an array, you may do something like:
throw new MissingSuperweaponException('We heave no nuclear weapons awailable!');
Than, somewhere at a higher level of your application you can catch all these exceptions and show the user the nice messages you want.
Please note, that exceptions are for exceptional cases, for situations in which your application should never be. Use then only when needed.
When there is a result of an operation, a result which can be TRUE or FALSE or a value or a string, that is not an exceptional case, that is a result or a return value. For example, when you do a search for a string the result can be the index of the searched text. However, not finding the text is not an exceptional case, you should just return zero or false, not an exception.