What is the ruling on burning religious papers, and what about the ash that results from that? And is it obligatory to bury all the ash, even if it mixes with soiled soil? And is there a sin incurred by that?

Papers containing revered religious texts should be preserved in a respectful place, or buried in a clean place, or burned, or completely shredded. If papers containing religiously revered texts are burned and their letters vanish, turning into scattered ash, then the objective has been achieved, which is the effacement of the letters. There is no harm in discarding the ash or burying it anywhere, as long as the letters have disappeared. The purpose is to respect the revered written material and prevent its desecration, and this has been accomplished by effacing it through burning. There is no sin upon you in what you mentioned, and the scattering of ash after burning does not cause harm.