Could a cell grow large enough to engulf your school answers

No. A single cell would have limited growth based on its DNA. The DNA supports the growth of the cell up to a point, but as it is a control mechanism, as some point a cell would be stopped from growing by the DNA because any larger and the DNA would not be able to control vital functions like transmissions of materials within the cell and also across the cell wall to do things like bring in food and take out waste.

Cell division is important to single celled organisms because it allows the cells to reproduce. through cell division, cells make exact copies of themselves. when single celled organisms go through cell division, they make exact copies of themselves which is how they reproduce.