If it was understood that the customer paid the money for you, then you can take it. If he intended to give it to the store, then it should be given to the store.
The mentioned tradition does not mean that the mother has more rights over the child than the father. Some narrations indicate that being good to the mother is more emphasized than being good to the father.
A woman must wear the hijab during work and in other places in the presence of non-Mahram. However, if she decided not to, she will be a sinner, but this does not affect the lawfulness of the income that she receives for such a work.
If the taweedh consists of supplications and verses of the Quran, then it is permissible.
There are lots of zyarats reported by the Ahlulbait (Peace be upon them) like Jamiaa, Warith and Ashura also there are lots of supplications like Kumail and the supplications of Sahifatul Sajjadia.