Is it obligatory for the sister to dispose of the things she bought with the money she received for designing a website for an official newspaper that sometimes publishes decisions containing religiously forbidden matters, and that is after she has already donated an equivalent amount from other money?

The money earned from designing the website is not considered unlawful based on what was mentioned about the website's status. The sister is not required to dispose of what she earned from this work, as the obligation on the earner of unlawful money is to dispose of only the amount of the forbidden money, and not the things purchased with it.