A trustee/creator passes away in 2023. He used to claim the trust income & expenses under his 1040.

1- For 2023 tax return should the trust be filed under the Decedent trustee 1040 or file 1041 under Successor Trustee?

2- The successor trustee sold stocks from the trust & distributed the proceeds among beneficiaries, should the basis of these stocks be The initial cost of the asset when it was first acquired or step-up Fair Market Value at Death?