3. You only need F1310 when a refund is coming. 

2. In my experience,  the IRS asks 3 or 4 times for F1310, so keep mailing it in. Makes several signed copies; you'll need them. They ask even if you e-file it. I'm not sure it is included in the e-file.

1. Since the TP died before the 2021 return is filed, who else but the Executor can sign in? E-filing is not supported from the beyond.

4. See 3. above.