Despite intensive research efforts, understanding how water freezes remains an open and relevant question with profound implications. In this study, we examine ice Ic nucleation and water relaxation at the atomic level, employing molecular dynamics (MD) simulations and Classical Nucleation Theory (CNT). Our key findings address the following foundational issues: (i) Routes to cubic ice. Ice Ic seeding liquid water results in equal amounts of ice Ic and Ih structures at T<235K, while ice Ic predominates at T⩾235K along zero isobar. Moreover, ice produced from spontaneous nucleation at T=205-215K is more cubic compared with that grown on ice Ic seeds; (ii) CNT validity. Using MD-generated data, CNT accurately predicts ice nucleation rates without any fitting parameter, thereby bridging the gap between simulations and experiments; (iii) Kinetic crossroads. We determined a kinetic spinodal for high-density water as an intersection of relaxation and nucleation time curves at TKS=199K for a MD sample and TKS=233K for a macroscopic sample, which coincides with the experimental homogenous freezing limit; (iv) Kauzmann conundrum. Finally, we indicated that if the Kauzmann temperature exists, estimated as TK=190K, it might be inaccessible for high-density water due to the kinetic spinodal at a higher temperature, TKS>TK, thus resolving the long-standing entropy paradox. Overall, this research provides valuable insights into fundamental aspects related to water crystallization.