Are sins and transgressions considered a form of trial, and if so, will the one who commits them enter Hell, knowing that a trial through illness expiates sins, whereas a trial through disobedience increases sins?

Sins are a type of trial, by which Allah tests His servants to see whether they will abstain from them or not. The trial of sins involves testing the servants' obedience to their Lord by refraining from them despite having the ability to commit them, not by engaging in them. As Allah states: "And ask them about the town that was by the sea - when they transgressed in [the matter of] the Sabbath, when their fish came to them on their Sabbath day, appearing on the surface of the water, and the day they did not observe Sabbath, they did not come to them. Thus did We test them for their defiance." (Al-A'raf: 163). So, whoever obeys Allah has succeeded, and whoever does not obey has failed and lost. As for entering Hellfire, it depends on the fulfillment of conditions and the absence of impediments.