Given that the car belongs to your grandmother's estate, what would make you think you'd be entitled to do that? Did she leave the vehicle to you in her will?
Why? The authority conferred on him by the power of attorney terminated the moment your grandmother died.
An affidavit that says what?
If nothing else, her estate includes the car you're driving.
I assume this means two cars other than your grandmother's car. Correct?
I'm not really sure that your insurer will care about your grandmother's death and consequent inability to sign anything. However, if the subject comes up, you obviously should not lie about that. You should, however, let your insurer know that the two people making a claim against your policy have "demand[ed] an [a]ffidavit from [you]."
Since you didn't tell us what this affidavit does or might say or why the two claimants "demanded" it, we have no conceivable way of intelligently opining about this.
Whether you do or don't sign some affidavit has no bearing on whether "they have grounds to take [you] to court." They have grounds to sue you because they were (allegedly) injured as a result of your negligence.
You don't know that. All you know is that you observed no injury and that no one complained of an injury. However, soft tissue injuries may not be immediately apparent.
Somewhere in the process, you were asked to identify the registered owner of the vehicle. That said, I disagree that this will have any impact on your coverage. It's not material.
Neither. It has no bearing on either your vulnerability nor your potential liability.

