In order to get the correct information call the Labor Board. In California no one gets paid for their 30 minute break. In California a full time employee is defined in the employee handbook, usually one who works on an average of about 40 hours a week (not counting 30 minute break times).
It's a fact of life most nursing homes have to make cutbacks in order to survive financially. If they cannot make money then they will be out of business and things will get worse and people will loose their jobs altogether. It does screw up the nursing hours not to mention demonstrates a lack of responsibility when employees do not clock in & out on time.
When census is low, and most of the patients are on medicaid it is hard for the nursing homes to make money.
Make up your mind what it is you want from a job if it is full time hours and benefits, then dont accept a position unless that is offered to U.
If I was in your situation I would look into the companies policy on write ups, usually the policy requires a supervisor to give you a verbal warning first. If someone violated the policy you could put a formal grievance in writing and see if the write up could be removed from your record.
Sounds like your unhappy and would be happier working for a facility that had the hours, benefit and a better attitude towards the staff.