Assuming you are the only heir, it's your house now, even if the deed has not been changed at the recorder's office (although get that done anyway). As the owner you can deduct the mortgage interest and property taxes as long as you actually pay them. (You probably need to notify the bank of her death and they will want you to refinance or legally assume the mortgage, but that is not a tax matter.)
Repairs and insurance are not tax deductible.
Your cost basis is the fair market value on the date of her death. It will be a good idea to document that, a qualified appraisal would be best, a market analysis by a real estate agent might be ok.
Improvements that extend the useful life of the property or increase its value can be used to increase the cost basis, but repairs do not increase the basis.
If you sell, your capital gains are the difference between the selling price and your inherited cost basis plus adjustments for improvements. If you never use the home for business or rental, you can get the first $250,000 of gains tax-free.
If you rent the home, you can deduct repairs, insurance, mortgage interest and property taxes as rental expenses against the income. You also deduct depreciation (wear and tear). But, some of that will be taxed when you sell, and if you rent it longer than 3 years, your gain will be taxable at that time as well.
