Yes, and this time don't wait for them to call you back. A week after you give them your application call them and see if they are willing to interview you. Show initiative. Employers generally like that until you actually work for them. Then the only kind of initiative they like is if you take on more and more and more and more and more work until it kills you and they don't have to pay for your health insurance or vacation benefits.
Sure. Probably they filled the previous position but a new one could be coming available. Apply every 3 mo until you get a job there if that is your dream. Get to know the manager if you can so you are at the top of their "I know someone for this job" list.