Regarding depreciation, when I enter the cost basis on the 4562 worksheet it does calculate deprecation for the short 3 month period. I also entered the Dec sale date (and proceeds), so the software "knows" I sold it within the same year. So, am I not allowed to claim depreciation?

Maybe, because the inherited property is deemed to be held long-term, the acquired and sold in same year rule doesn't apply. Or maybe the software is wrong. I don't know.