Is it permissible for a woman whose husband has passed away to go out with her brother to buy household necessities from the supermarket during the 'iddah period?

If you need to go out with your brother to buy necessities, there is no sin upon you. A woman in 'iddah is permitted to go out during the day for her needs, whether she is divorced or widowed. The fact that she can find someone to fulfill her needs does not prevent her from doing so. There is a view among the Hanbalis that permits her to go out during the day for her needs and other matters, but what is more cautious and absolves one's responsibility is not to go out except for a necessity, and not to go out if she finds someone who can suffice her.