I have no way of explaining why "gas", "electric" and "heat" would be separate. Normally the cost of running your gas furnace would fall under your gas bill, and electric heat under your electric bill.
You can ask that she provide you with receipts to support her claims. I don't know if she'll provide them; from what you've said so far, I expect not. If she sues you and you defend against the suit, the court will expect her to document her claims.
You and your husband are both students, so you may have a "student legal services" organization available to advise or assist you. Check with your school.

