1. Can you please provide further detail. Did your Mum die leaving a will or not? If she left a will, what were the terms of her gifts to you? Did anyone else inherit? Who was the residuary legatee?
2. You will not be personally liable for your Mum's debt to the mortgage company if there is not sufficient on the second property's sale to pay off the mortgage. It will be your Mum's estate which will be liable to pay off the remainder of the mortgage. This debt owed by the estate will have to come out of whatever assets were in the estate at the time of death. It cannot just be transferred to the property you now own. HOwever, if the executor made a mistake in transferring out a property without there being enough in the estate to pay all debts, then the executor will be liable. However, if there are assets in the estate, it means that the person who takes the residue left after the specific bequests have been given out - known in law as the residuary legatee - who will have their share diminished.
3. Yes, your aunt the executor could be liable. And yes, your aunt could sue you if there was an overpayment.