Many dicots have taproots, monocots do not. No, the root hairs would be torn off by elongation of the root. It is a simple central cylinderin the root but more complex in the shoot.
Lateral roots break through the cortex on their way out but they arise from deeper within the root.
The pericycle is just inside the endodermis and remains meristematic. Right, if they formed ahead of this zone they would be torn off as the tip advances through the soil. Once they are in the pericycle, water and solutes can take any path to the xylem. Yes most of the root mass is cortex which is made up of parenchyma cells and provides a site of storage of starch and organic nitrogen compounds. Internodes have less meristematic potential than other parts of the stem.