To answer questions:
1. I don't understand why the estate EIN changed but the estate was for the full year, you just want to use the new EIN.
2. Yes, enter the income.
3. A 1040 is only done for the year of departure.
4. Filing returns for prior years may yield a refund.
5. Dealing with this is complicated. At some point, you will probably need to file a final estate return.
My disclaimer and thoughts:
I think you are saying that no estate returns were filed and there was an EIN. You got a new EIN for the same estate. The beneficiaries never received k-1 statements since estate returns were not done.
The paperwork in your dad's name is part of his estate. Page 4 of Form 1041 instructions lists items that are income in respect to the decedent. For nominee, see Responsible Parties and Nominees.
You may be safe to file the return without worry and get things switched over quickly to the estate or closed out.
You can file back returns for the years missed. Enter 1041 and the year to get the forms and instructions. I think once you do this year, you can go backwards easily. For this year, you need TurboTax Business. Beware, you don't want to generate k-1 forms for the past, since that would force you to amend your personal returns.
You may be able to get refunds by filing. You may decide the cost of the business software, the hassle of the estate, doing the k-1 forms and filing is not worth a $44 refund. The IRS should not bother with you without a tax liability.
You do want to get things moved to beneficiaries and get the estate settled. You will want to file the final estate return showing k-1 distributions, if any.
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