Generally, an employer can reduce your shifts or cut your pay without cause.
There are several exceptions, though. If you feel like something just isn't right, then you should trust your gut and contact a lawyer for a consultation. Usually lawyers will give you a free initial consultation to see if you have a case.
As for your salary, it sounds as though you are classified as an "exempt" employee, i.e. salaried, not hourly in pay. You should also talk to a lawyer about this, as if you are wrongly classified, you may be entitled to back wages and overtime.