No. Property owners can rent to tenants who have not completed an application. However, it is recommended to use such an application if you plan on doing your due diligence about the prospective tenant first, including obtaining permission to inquire into their credit history.
Yes. Property owners can reject any potential tenant for any lawful reasons, which include not completing a rental application.
No. A prospective tenant can change their mind as a Residential Rental Application is not a legally-binding document.
No, a landlord cannot compel anyone to provide their social security number, and they can run a credit check without it. However, a landlord is still allowed to reject the rental application of someone who refused to provide the social security number.