Yes, you are correct. A form 1041 is not required since the income is below $600 for the year. If any amount remaining belongs to the beneficiaries, it should be disbursed as well. For this reason you will have no reason to file 1041-K1 to issue to beneficiaries.
If you applied for a EIN for the trust, once you are certain there is no income to report or distribute any longer you should file a first and final on the same return, just to close it out completely. You can wait to do that for 2025 so you are certain there will be no further activity in the trust.
For Arizona (AZ), the income will carryover from the federal AGI and unless there is a accepted subtraction the income will be taxed there as well. AZ does not have an estate tax.
IRS FAQs for Life Insurance (would be the same for AZ).
Generally, life insurance proceeds you receive as a beneficiary due to the death of the insured person, aren't includable in gross income and you don't have to report them. However, any interest you receive is taxable and you should report it as interest received.
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