Princess Mononoke/WMG

Moro's mate...

 * is Fenris, from Norse Mythology. Because they are both giant wolves!

The pelt that San wears is a wolf pelt.
Before Moro attacks the humans for "defiling the forest", they had found her puppies and killed one of them. Then the humans sacrifice their baby so they can escape. (Whether they actually escape or not is unclear.) So Moro decides to raise San as her own to replace the pup that she lost. The pelt is from the dead puppy so San could stay warm.
 * The ears and mask put on it were so that San could hid her human features which she detested. She grew up with a warped sense of beauty, never considering herself to be so. This is why it shocked her so much when Ashitaka said that she was beautiful.

Princess Mononoke and Valley of the Wind take place in the same universe.
Princess Mononoke being the past and Valley of the Wind being the distant future. Nausicaa is a descendant of San and Ashitaka. She inherited her love of nature from San, her desire for peace from Ashitaka, and her fighting ability from both of them.
 * Who's to say Valley of the Wind didn't happen first, in an even more distant past?
 * Because they specifically say that Ashitaka is an emishi, an indigenous group from northeastern Honshu. They're a dying race today, so they would be wiped out by time Nausicaa takes place. Princess Mononoke takes place in feudal japan.
 * Also, compare the spirit forest to the petrified forest under Nausicaa's toxic jungle.

The Forest Spirit...
Set all of this in motion, resulting a huge Batman Gambit to lure Ashitaka there in order to bring peace to the forest and the humans.
 * More like a Thanatos Gambit, since the events led to his death.
 * He can't really die, remember? He's the Anthropomorphic Personification of the natural cycle of life and death, after all.

the movie takes place in the same universe of Avatar...

 * Cold Sniper and Knife Nut skills, sheer badassery, sense of responsibility for the troops...Lady Eboshi is probably an ancestor of Colonel Quarich.
 * the Forest Spirit could be a manifestation of the forest's Hive Mind, an ancient yet gone terran equivalent of Eywa.
 * Can't be - There's too much Gray and Grey Morality out there. Avatar was as Black and white as a Rorschach test.

Lady Eboshi is either an ex-brothel girl herself, or was abused by a man at some point.

 * that's why she goes out of her way to get brothel girls to work for her-- giving them work and mobility they'd never have otherwise-- arm the women-- so they can never be hurt. My guess is that she was in a bad marriage and escaped, if her upper class accent is anything to go by.
 * Word of God says that she was a slave on a ship who successfully mutinied and freed the others.

Moro's mate is the Party God
.
 * Because a severed wolf's head can still bite. This particular wolf deity head survived (whereas his mate dies). Years later he would give up the whole protect nature shebang (probably after the Murshroom Wars) and dedicate his life to partying.

Gods becoming demons

 * Being shot doesn't turn the animal gods into demons. It essentially allows a pathway for evil spirits to take hold on their bodies. Notice how Nago shakes off the corruption at one point at the beginning of the film. He himself hasn't become a demon but he has been possessed by one.