Is the seller of silver on installments to women sinful, knowing that some of them are not veiled and may wear these ornaments outside the home? What is the ruling on stores that sell these ornaments to women in general, and if there is a sin upon them, from where do veiled women buy ornamental jewelry?

There are two issues in the question:

First: Selling gold or silver jewelry in installments is not permissible.

Second: Selling jewelry in general is permissible, based on the generality of Allah's Almighty saying: "And Allah has permitted trade." However, selling it to someone whom the seller knows will display it uncovered (tabarruj) in front of non-mahram men is not permissible, because displaying a necklace is an inner adornment that is not allowed to be shown to non-mahram men. If the seller knows that the buyer will display it uncovered in front of non-mahram men, then selling it to her is forbidden, based on Allah's Almighty saying: "And do not cooperate in sin and aggression." However, if the woman's situation is unknown, the default is permissibility.