Autocomplete Extender "No item found"

Answer 1

I'd say a null response or preferably an empty list clearly communicates that nothing was found, in a search method. How you want to handle that is a matter of presentation, and that should not be dealt with at all from your service. Check for null or empty lists (whatever you decide on) in your handler function

Answer 2

You can refer to that article Check if AutoComplete list has result items, it will help you to check if user input doesn't cause any result items from AutoComplete.