We know Avada Kedavra affects a person's metaphysical soul. It rips the spellcaster's soul apart.
Are there other curses that can affect one's soul, say the other unforgivable curses? Is Avada Kedavra the only curse that affect the caster's soul?
Casting the spell Avada Kedavra is not, in itself, what rips the soul in the world of Harry Potter. What does that is murder. See: Is murder a necessity to detach your soul? Logically, therefore, any spell that was used to murder someone could have the same effect.
Dumbledore even suggests that it might not damage Snape's soul to use Avada Kedavra to kill Dumbledore according to his plan. Presumably, Dumbledore thinks this because he thinks that it would not morally constitute murder:
“That boy’s soul is not yet so damaged,” said Dumbledore. “I would not have it ripped apart on my account.” “And my soul, Dumbledore? Mine?” “You alone know whether it will harm your soul to help an old man avoid pain and humiliation”
Per the answers to the first question, there doesn't seem to be an known alternative to murder as a means of splitting the soul, but after it is damaged, the Horcrux-making spell is what separates an already-torn soul piece and encases it in some external object.
And on the other hand, remorse can repair the soul:
“Remorse,” said Hermione. “You’ve got to really feel what you’ve done. There’s a footnote. Apparently the pain of it can destroy you. I can’t see Voldemort attempting it somehow, can you?”
The wizardingworld.com article What is the story behind each of Lord Voldemort’s Horcruxes? indicates that each horcrux contained a soul fragment that was split by a single specific murder that Voldemort had carried out relatively recently prior to the horcrux's creation. Several of these murders were not performed by means of Avada Kedavra. E.g. the article states that the diary horcrux was created after Riddle's soul was split by murdering Myrtle, who died from seeing a basilisk, not from Riddle casting Avada Kedavra on her.