Do I have to file a tax return and a trust tax return in January?

Your trust, especially for its first two year, does not need to use a calendar year. Even if it did, the first return would not be due until March 15. Likely you have a deductible loss on the sale and will benefit by using a later year end, such as September.

You would be required to file an income tax return for your father for the period from January 1, 2013 to date of death if he had sufficient income to require filing. The return would be due April 15, 2014. You can elect to treat the trust as part of his estate for up to two years from date of death, in which case you could file an estate income tax return using a fiscal year from date of death until September 30, 2014, which would include the income of the trust. In that case, the first 1041 income tax return would be due January 15, 2015. Alternative, you can just file a trust income tax return. The trust's first tax return, then, would be from date of death to December 31, 2013 and the first 1041 income tax return would be due April 15, 2014.