Is it permissible to eat from the money of someone who owns a cafe that serves shisha, and has no other source of income?

It is not permissible to open a shisha cafe because shisha is forbidden, and the money earned from it is forbidden. As for tea and permissible items, there is no harm in selling them.

One should advise the sister's husband gently regarding the impermissibility of serving shisha and the harm of consuming forbidden earnings.

As for eating from his money, its ruling is that of mixed money. The preponderant opinion is that it is permissible to deal with it, though disliked. It is better to refrain from eating from his money and accepting his gift.