Mnemosyne/WMG

Yggdrassil is Mnemosyne.
Mnemosyne was the personification of memory in Greek mythology. Time spores are produced by Yggdrassil and contain the memories of the people they infected. As long as an immortal's time spore is not destroyed, they can regenerate any amount of body damage - i.e. their memories, preserved in it, rebuild the bodies from scratch. Therefore, the "Daughters of Mnemosyne" are the immortals, though how they relate to Muses is still unclear...

Angels Don't Age.
Unless an angel is killed (and they are as vulnerable as baseline humans), they can have an unlimited lifespan just like the immortals. The only problem with that is that angels tend to give in to their primal savageness and start attacking immortals on sight, which doesn't exactly increase their longevity... However, as Shogo's example clearly showed, a strong willpower can resist the primal urges for a long time and this is probably what happened with who survived for many centuries, eventually learning to control himself completely (or maybe his being  helped).

It also seems that the older the angel, the more powerful his presence is to immortals. is millenia old and Mimi could barely stand 20 meters away from him and he wasn't even in his angelic form yet.

Angels are a safety mechanism against Immortals
Yggdrasil realized that if left unchecked, the Immortals would eventually enslave or exterminate humanity (like Sayara tried to), so it created the angels as a counter-force of sorts. The angels' only function is to decrease the population of the immortals but hunting and destroying them, which is why they are stripped of anything but the basic instincts and given superior equipment (wings, sex aura) but not invulnerability in any form (Yggdrasil has enough time spores).

This is somehow connected to Ah My Goddess
Yggdrasil is a giant computer. Immortals are, more or less, bugs in the program that creates Time Spores to record all data in existence. This just happens to be the part of the universe where all of the excitement gets dumped.

Rin is the ancestor of all Time Lords
That built-in link to Yggdrasil that all of humanity will eventually have? Yeah, it turns them into the first Time Lords. Regeneration is a watered-down version of the benefits of eating a Time Fruit.
 * Or conversly, Yggdrasil was created by Time Lords as a way of studying humanity.

Rin is realted C.C., and the code is part of Yggdrasil
The green hair, regenerative properties she has and the fact that she can revive from just about anything are definitely very simiar. Her green eyes remind me more of Sonozaki Mion/Shion however.

If a sequal is made, the antagonist will be...
Nidhoggr, or an expy there of. This being will be neither angel nor immortal, but something more closely resembling a dragon, and will set about slaughtering Rin's descendants to slow or halt the spread of the link to Yggdrasil. This will be an adaptation of Nidhoggr's role in the original norse myth; to contain the spread of the roots of the world tree before they outgrow the boundries of the universe. This character will be played as a Knight Templar or Anti Villain, given sympathetic qualities, and be potrayed as large, physically powerful, and decidedly nonhuman to contrast sharply with Apos, giving Rin pause as up until now she's only had to fight against complete monsters.