Job applacations

Yes, they can: any person may ask any other person essentially anything they want. And since there is nothing confidential about the reason you left employment--unless and only if your employer signed a confidentiality agreement about this--your ex-employer is free to answer them. That said, your ex-employer is not required to answer: they are free to ignore the request.

Checking a job candidate's work history references is a common practice in the hiring process. So a prospective employer contacting a candidate's former employer is perfectly permissable. In fact, most job applications give specific notice as to this (although it is not required). Further, an ex-employer may say much it wishes about a former employee but risks a defamation lawsuit if it makes statements that it knows to be false and which it reasonably should have known would cause damage to the former worker. Specifically, in CA, an ex-epmployer can make statements about job performance, qualifications, and the like. However, statements regarding an employee's constitutionally protected free speech or activities or comments regarding a former worker's union or other concerted activities, is not protected.