You can use "inherited" for the date acquired (since the securities were technically acquired on the date of death).
The estate is not required to file a return for the tax year in which it has less than $600 in income, so that is not problematic (it can be explained in a response to an IRS notice if such notice is ever received, which is highly unlikely).
You can enter the total amount distributed, but only the actual gain or loss (if the return is the final return for the estate) will appear on the K-1s.
