Is it permissible to write and publish purposeful social novels that depict characters as religiously and morally committed, and what is the ruling on the financial compensation resulting from them?

Writing novels falls into three categories:

The first is that they contain something that goes against Islamic law; in this case, they are not permissible.

The second is that they contain something that serves Islamic law; in this case, they are recommended.

The third is that they contain neither of the above; in this case, they are permissible.

It appears that your mother's novels fall into the second category, so there is no harm in writing and publishing them, and she will be rewarded for it. It is advisable to show them to trustworthy preachers or Islamic literary figures before publishing them. Financial compensation is permissible.