Those kinds of clauses are illegal in states like California and Arizona. You or your employer can terminate your relationship at any moment without cause.
Not true. At-will employment is more of a default than a binding rule. In other words, you and your employer may have a contract that sets more specific rules than what at-will employment requires. However, if you don't, then it is implied that you are employed at will.
A contract can say any thing but courts will enforce only certain things.