Is providing water (a water fountain) considered an ongoing charity (Sadaqah Jariyah) for the deceased if their children undertake it after their death, and is contributing to the building and furnishing of mosques among ongoing charities?

Providing water, if it is by digging a well or creating a river from which people benefit while its source remains, is an ongoing charity (sadaqah jariyah). As for building a water fountain for a fee, it is not considered such; rather, it is a charity from which the deceased benefits. Contributing to the construction and furnishing of mosques is among the greatest ongoing charities, because it is something from which people benefit while its source remains. It has been explicitly mentioned in hadiths, such as those narrated by Al-Bazzar.