The EIN would be for the estate.  

If there is a probate you will need the 1310 along with the court order, and it will have to be paper filed.

If no probate then the 1310 will need to be added to the return and can be efiled.

Any refund will be by paper check, no direct deposit option and depending on if a probate is being worked then the refund will be made payable to the estate.

And if paper filed, it is going to be a while, filed one in March right before the shutdown, still no refund in site as nothing is getting processed.