coming to grips with estate income tax 1041

Okay, so any income received by my spouse after her death is taxed to her estate, right? I calculate that the fiscal year ends April 30 and the 1041 is due August 15, right (assuming no extension).

Now, I don't have to pay the awful "kiddie tax" tax rates from the 2017 tax legislation if the money is distributed to the beneficiary, right? And I'd declare her total income and then pass it through to myself on a form K-1 so that it will appear on my 2024 tax return?

Can capital gains be passed through to the beneficiary as well? I gather that in the case of a trust, it's the trust that must pay the capital gains tax, but that doesn't seem to apply to an estate that will end in the present calendar year.

I file a Schedule C as self-employed. Can I bill the estate for the time I spend on the estate 1041?

I'll be grateful for any and all answers, and for deductions that haven't yet occurred to me. Thanks! - Dan