Legal Question in Real Estate Law in California

If the mortgage was in your father's name "as trustee" of the trust, the successor trustee named in the trust documents should be able to take over the mortgage. If it was not "as trustee" then your father's estate is responsible and when the estate is administered the mortgage will have to be refinanced or paid. A final personal income tax return will have to be filed as part of administering the estate. The interest to the date of death will be deducted on that return. After death the deductiblity of mortgage interest becomes a specialized estate taxation issue that I am not qualified to advise on. If the trust permits the condo to be distributed out of the trust to the beneficiaries, you and your sister will have to agree who gets the deduction. The IRS does not allow co-owners to split mortgage interest between personal Schedule A's. In the alternative, if you rent the property out, you could file a partnership K-1 to divide the profits/loss and that would include splitting the interest. If you distribute the property out of the trust, whether or not you buy your sister out, the lender will most definitely require you to refinance.

The trust or the beneficiaries better pay the mortgage or it will be lost to foreclosure. Your other questions will have to come from tax and law experts, after full review of the trust and other facts. Consult with a local attorney as a start.