Is it obligatory for me to teach worshippers who make mistakes in their prayers, and does this fall under the hadiths "Whoever among you sees an evil, let him change it with his hand" or "Whoever conceals knowledge will be bridled with a bridle of fire"?

If the errors committed by some worshipers are of the nature of abandoning a pillar (rukn), an obligation (wajib), or an act that invalidates the prayer, then it is incumbent to advise and teach them. However, if they are of the nature of abandoning a recommended act (mustahabb) or committing a disliked act (makruh), then it is recommended to teach them, but not obligatory. Enjoining good and forbidding evil is obligatory when it pertains to abandoning an obligation or committing a forbidden act, but it is recommended when it pertains to abandoning a recommended act or committing a disliked act.