Sale of Inherited Rental Property - Ordinary Loss?

My mother-in-law passed away in September 2023 and we inherited her 4-flat building (which was titled in the trust). 

 

  1. The building sold on Dec 22, 2023 for $725K, so I will also use that as the basis. Can I depreciate the building from her date of death (on Sept 23) through Dec 22, 2023 (3 months)? 
  2. Because of closing costs, there will be a loss of approx. $50K. Would this be a Sect 1250 loss (ordinary)?
  3. All proceeds will be distributed from the trust bank accounts in early Feb 2024.