[Manardariel]

Galadriel survived for three reasons. The first one is her probable (at least partial) innocence at the kin-slaying. The Doom of Mandos to my understanding only applied for those that were directly involved, which would mean that from that point on Fingolfin and Finarfin´s sons also also doomed. Finarfin himself didn´t fight in Alqualonde, which explains why he was pardoned by the Valar. In both version Mithadan suggests, Galadriel is -more or less- inocennt, so the doom of Mandos didn´t count for her. She was less doomed to suffer than herbrothers, who were killed in the Was of the Jewels.

Another reason is that Tolkien wanted to point out the Wars of the Jewels weren´t totally hopeless. Not everybody died, in fact a princess of the Noldor who was involved in the rebellion didn´t. This is a powerful sign, for it suggest hope as well as the forgiving of the Valar. Galadriel
was involved in the rebellion, but she never let blood touch her hands (as far as we know). The Valar and Eru let her live to show that they weren´t totally unforgiving, and tha the War of the Jewels wasn´t totally futile.

Galadriel also functioned as a reminder of the Eldar´s past in Third- Aged ME. In a time when only few people, even elves, remembered what had happened some milenia before their birth, someone who actually had seen it all was a powerful reminder. Galadriel´s memories were essential to her when she agreed to carry Nenya. Remeber that Gandalf was a Maia and Elrond the heir of two half- elves and some great lineages. Galadriel was one of the oldeast Eldar in ME and her powerfull memories helped her carry the burden of a Ring of Power.

In Galadriel´s past we find memories, pardoning, innocence and determination all combined into a strong female character that was able and strong enough to live through three ages of ME.