You really do need to consult with local legal counsel and a local tax professional.
See https://taxexperts.naea.org/listing/service/estates-gifts-trusts
See https://www.avvo.com/estate-planning-lawyer.html
Regardless, and generally, an estate is not required to file an income tax return unless it has gross income of $600 or more for the tax year.
See https://www.irs.gov/instructions/i1041#idm140229151947712
Further, irrespective of the date of death, the personal representative (or individual responsible for filing a Form 1041 for the estate) can select a fiscal year when the estate files its first income tax return.
See https://www.irs.gov/instructions/i1041#idm140229123435296
1099s are based upon calendar years, so you would issue any required 1099 in the calendar year in which the proceeds are paid.
The K-1s will follow the ending date of the estate's tax year.
