I am sorry about your loss.
If the house were solely in his name, the house is still in your father's estate. If he had a Will it passes to the beneficiaries named; if not it passes according to the state's law of intestate succession, and probably goes to you and your mother. (I do not know TX law.)
As the property was not transferred to your mother before her death, HER SHARE obviously can not go to her, instead it goes to her estate; if she had a Will it goes to her named beneficiaries, if no Will, to her heirs at law -- probably you and any other children or their descendants.
You'll want a lawyer to straighen this out -- I promise it is worth it, and that will give you title that you can convey to a buyer of the property.
Your mother's estate is liable for the bills, and as she owned the house, you'll have to pay it out of her other assets or the estate -- if there are no other cash assets, you may have to advance the money yourself to pay the bills as if they turn off the power, it will be harder to sell the house -- although the lawyer you get will have some ideas on how to handle this.