Aurelion Sol's lower body is not part of his in-game hitbox, which is why it is semi-transparent.
Starsurge is almost tied with Hawkshot for potentially the longest-ranged basic ability. As long as Aurelion Sol keeps up with Starsurge, the star will be able to travel from one end of the map to the other.
Ao Shin had an ability resembling a global-ranged Resonating Strike: he would send a storm cloud in the target direction, marking enemies hit and allowing him to dash to the target as a massive bolt of lightning (the idea showed enough promise to be picked up in the future)
Primary inspirations were The Great Owl from The Secret of NIMH (for being awe-inspiring and whose power and wisdom are worth the risk of seeking out) and David Bowie (for his effortless, marvelous, and beautiful demeanor, his 'inspired' creations, and his 'justified' rockstar arrogance)
At one point Aurelion Sol had a really elongated body, described as 10-12 Teemos in length, which people naturally wanted to use to snake between and coil around their opponents.
However, this body ended up taking up most of his power budget (he'd have to be really fast to constrict his opponent and/or durable to survive the try) as well as causing technical concerns relating to brush concealment.
Aurelion Sol is a cosmic being capable of creating and destroying stars with the flick of his fingers.
When Aurelion Sol dies he dissipates into a dragon-like constellation. Whether or not this has lore significance regarding Celestial dragons is unknown.
It however proves his kind is not immortal, as he himself pointed out.
Celestial dragons might be related to terrestrial and elemental ones.
According to a Q&A with Riot about Aurelion Sol, it is mentioned that during his story's development they had an idea that some of the 'celestial beings' that Aurelion mentions were actually his sisters, whom control other aspects of space such as Gravity or Dark Matter. Whether or not this is still canon is unknown.
Though this is further implied by when Swain strikes Aurelion Sol with Ravenous Flock, asking him "What is this about... siblings?".
e"Love is as real a force as gravity. Try it once in a while" might be referencing Amelia Brand from Interstellar, who talks about how both love and gravity transcend time and space.
This skin may also be a reference to the Dark souls franchise
As one of the oldest living beings in the universe, Aurelion Sol has witnessed the rise and fall of countless worlds and civilizations, but the world that peaked his interest and curiosity was Runeterra.
Mount Targon has direct cultural and historical ties to him, being the highest and therefore most accessible location for him to act from as well as being the Aspects' homeland.
Aurelion Sol despises them for deceiving, enslaving, and figuratively clipping his wings to use him as a weapon against the Void and any other resistance, a pet on a leash. If he so much as insubordinates, the Aspects destroy one of the stars he tenderly and lovingly crafted to light up the cosmos. This arrogance on their part has earned them Aurelion Sol's spite and contempt, so much so that he wants nothing more than to see Targon's fall.
This is why he fancies neither Diana nor Leona (whom he sees as naive and foolish for putting his creations on a pedestal) and especially Pantheon (whose incarnations have a tendency to bark orders at him)
Aurelion Sol has knowledge of Bard, Kindred, and Nagakabouros.
The village sage from Bard Mountain (Ionia) was convinced his people would die without the Celestial artifact Noxus was after and Bard snatched away. This artifact's relation to Aurelion Sol is uncertain.
Aurelion's quote: "The depths of space crawl with terrible entities. Pray they ignore this world." may be referencing the Dark Star Entities. They being cosmic entities who devour worlds and stars, serving as Aurelion's polar opposites.
Zoe speaks to him as though he were a pet of hers.