All this will happen within an already existing mutually catalytic network, which as can be shown mathematically, will favor some reactions and abolish others. But the major answer to this question - we still have to work hard to find out how this happened. This is legitimate - after all very pro minent fields of research such as the Origin of the Universe, galaxy formation, planet accretion, super novae and black holes are studied by such means. They display homeostasis - a capacity to preserve their properties, paticularly chemical concentrations of their constitutent components. Any organic molecules that form assemblies could trigger the process that led to life.
Life today is characterized by a very specific set of biochemicals.
It should be considered a very tiny corner of the chemical space that could embody life. There is no reason to believe that any limitations existed, except very broad solubility and reactivity constraints. It is very likely that the answer is Yes on both counts. Carbon is required for generating the huge diversity of chemical configurations essential for our scenario, and water is essential because it is a universal solvent, that could bring together dispar atye chemicals. But it also provided the flexibility embodied in coloid-like dispersions that may exchage component readily with the environment.