Mom had no will, no spouse, I am her only child. She has one sister alive, who has said and is willing to sign a paper that she has no interest in anything she has. Property taxes are paid with the mortgage payment, we have hazard and earthquake insurance. And honestly I'm not sure what deductability has to do with anything. The mortgage interest is only about 900, in the past year.
GET THE PROBATE DONE. There is no "deadline", but there are legal ramifications. The state does not like property to be unowned. Just because it might be yours does not mean it is yours. I can't find an easy case on the insurance issue. How do you carry the insurance? Who is on the policy? What type of policy(s) are there? I recognize that just because you don't have title to the property does not mean you don't have an insurable interest. The theory is so broad so as to certainly contemplate your situation being of some pecuniary value to you. BUT, when property is in a trust, the trustee insures it and not the beneficiary. When property is in an estate, the administrator insures it and not the heir.
Also, did your mother receive any Medi-Cal benefits?
If someone goes by and throws eggs at the property or someone trespasses, do you have the (legal) right to sue them? What if the neighbor's tree falls down and hits the house? You don't own the place, you don't have the right to deal with property issues. That may not be a problem for little things as the repairman will still repair without asking for proof of ownership, for big things it gets much harder. If the house were to get damaged, you may not be able to fix it or get permits or other legal permissions.
The deductability issue is probably unimportant as it seems you are not making much in income.
You are in a quasi-legal issue in regards to the property. Things can go wrong and this is what I see happening. You're going to wait for a few months to finish paying off the house to save up for probate. Then, once paid off, you'll have a little celebration that will put savings back a week. Then the car needs fixing and the water heater needs repair and that is a few more weeks to put off probate. After a while, you'll be living in what you believe is your house and there are no problems and everything seems fine. Because it seems fine, there is never really a lot of pressure to get the probate done as there always seems to be a greater need for your money than to pay for an attorney or to do the work on your own to get probate done. Then something happens. I don't know, any of a number of things. Say someone falls down on the stoop and cracks open their head and so they sue you. At least then you'll find out if a homeowner's or a renter's policy was the appropriate one to get.
How much is the estate worth? If under $150K you might be able to get a document preparation service to help you get things done for much less than you are thinking. Look into it. Get it done.