Bishul akum for the mother of a convert

Kashrut
1

Hello

concerning bishul akum is there any indulgence for the mother of a convert if she comes to visit him and cook a dish in his absence at home with the utensils and kosher food of the convert ?

thanks

2

I wish I can think of something. Sorry.

3

I understand that the food is considered bishul akum but what about the kelim in this situation. Do they require kashering?

4

No difference