Yes, you can be fired.  Unless you have a written contract, you're an employee "at will," which means that the company can fire you without having or giving any reason at all.

The only exceptions are for things like illegal discrimination (race, religion, etc.) and a few other things (one example is retaliation for filing a workers compensation claim).  There's nothing in your question to suggest anything like that.  If you have any information that suggests that discrimination was at work here, please talk to a local attorney.

It depends.  Generally the answer is yes.  As answered before, however, if you are employed under a written contract that prohibits this kind of termination or the termination is really based upon a bias against your race, gender, age, etc., the answer may be no.  Based upon the limited information in your brief question, your firing may not have violated any of your rights.