First contact the broker/banks asap and get the EIN from the IRS ... it can be done online and it is free. Then all income UP TO the date of death belongs on dad's final 2020 return. All income from the date of death forward goes on the trust return. Same goes for the CDs ... contact the administrator to alert them of the change of ownership.
I suggest that you read IRS Pub 559 (Survivors, Executors, and Administrators) for guidance.
https://www.irs.gov/pub/irs-pdf/p559.pdf
How to efile for a person who is deceased
https://ttlc.intuit.com/questions/1899441-can-i-e-file-a-tax-return-for-someone-who-is-deceased
You might need form 1310 to claim a refund for a deceased taxpayer
https://ttlc.intuit.com/questions/1899320-form-1310-statement-of-person-claiming-refund-due-a-deceas...
