Can 'had' be used in this sentence. Isn't 'have' appropriate with 'still' in this case?

You can use "Spielzeug" for a single toy, but the German here sounds more as if "Spielzeug" were a mass noun which would be translated as "the toys". For a single toy you would rather specify "die Puppe, den Teddy, das Puppenhaus ...".

Spielzeug as a mass noun is very common: "Räum dein Spielzeug auf." "Tidy up your toys."