In S, the nucleus is actively involved DNA replication in preparation for the next mitosis. Here each molecule of DNA is copied semi-conservatively. The two strands of DNA double-helix are held together. Meristematic cells, by comparison, rapidly cycle and it is likely that their G1 and G2 phases are rather short. Of course during interphase it is important to make addtional organelles and so on in preparation for the upcoming cytokinesis.
Mitosis means the division of the nucleus.
These consist of two DNA strands held together at the centromere and surrounded by proteins. The nuclear envelope will disappear, releasing the chromosomes to the cytosol. At one time centrioles were thought to organize the spinde. Moreover, destroying centrioles in animal cells does not disrupt cell division either. This is a relatively recent conclusion, but there is some evidence suggesting that centrioles are important in flagellum development.