Filing taxes for person who died prior to filing previous year taxes

My sister died the end of January 2023 prior to submitting her 2022 tax forms.  I have completed her 1040 for 2022.  I have a couple questions: 

1. Do I mark her as deceased on the 2022 form even though she was alive the end of 2022? 

2. She is due a refund.  I know she will owe some tax for 2023 so can I still carry that refund forward?

3.  Is a regular 1040 filed for her 2023 tax up until the day she died, then a 1041 estate return for the remainder of 2023?  So two tax returns?

When I say I know she will owe tax for 2023 even though she died in Jan 2023, it is not due to income.  She was paying household employees and withholding tax so will have to pay what she withheld to the IRS.