Dylan is in the process of adopting Arwen from an orphanage. He pays $$8,000$ in $2021$ and $$7,500$ in $2022.$ Dylan's AGI for $2022$ is $$165,000.$a$.$ How much is the adoption credit that Dylan may claim for $2022$ if the adoption becomes final in $2022?$b$.$ How much is the adoption credit that Dylan may claim for $2022$ if the adoption becomes final in $2023?$c$.$ How much is the adoption credit that Dylan may claim for $2022$ if the adoption falls through and is never finalized?