Can an Employer terminate the employment of any employee any time, with or without reason, with or without notice?

In general, yes.  Some employees have contracts (which can be individual contracts or union contracts) which limit the reasons and/or set procedural requirements before an employee can be terminated before a defined date.  However, most employees are employed at will, and can be terminated at any time for any reason that is not prohibited by statute (race, gender, religion, etc.)