You are free to set the deities of your world. See p. 10 of the DMG, under "Gods of Your World":
You can adopt one of these pantheons for your campaign, or pick and
choose deities and ideas from them as you please.
You need to pick their alignment, symbol, and domains. As an example, they might be chaotic neutral, have a roaring dinosaur ...
Her corpse will appear on the Astral Plane.
In DnD, when a god dies, their corpse will appear on the Astral Plane as a giant stone statue of them. These god-corpses are basically the only solid ground to be found there, and the Githyanki use them as the basis for building their cities.
Here's another SE question discussing the potential uses for the corpses ...
Oh, Very Very Yes
If you want some dead gods, come on down to the Avatar Trilogy, where Bane got Banedead, Bhaal rolled over, Myrkul went from being God of the Dead to dead of the god, and other such fun events. They're not the only ones - just some of the many who had themselves a very bad day during the Time of Troubles. Each one had the bad luck to be ...
Auril is featured in Icewind Dale: Rime of the Frostmaiden.
Auril the Frostmaiden is an antagonist in the adventure Icewind Dale: Rime of the Frostmaiden, which gives some info on what happens to her if she is killed: