Molecules typically diffuse from an area of higher concentration to an area of lower concentration.
Molecules will diffuse out of a cell if the concentration of those molecules is higher inside the cell than outside. This process involves moving from an area of higher concentration to an area of lower concentration.
The removal of wastes usually happens in cells where cellular processes produce waste products. This could be the cell where waste materials are transported out of the cell or where they are broken down.
The nucleus is typically the organelle that contains the genetic material (DNA) and is involved in controlling the cell's activities. In both cells, the structure that serves this function would be the nucleus.