If SGs are chosen by the stars (?) , is Aurelion Sol the one choosing them ?

hmmm idk Aurelion Sol creates stars, so idk if he is the one choosing them perse. It could be, but you also have to take intoa ccount that Sol-boi is basically enslaved by Targon and not capable of doing anything much.

I'm fairly sure it's First Star. We don't know much about them, just that they're the entity that overrules the Star Guardians, but if anybody chooses Star Guardians, it's them.