What is incumbent upon one who intended Umrah and exited his Ihram due to illness, then returned to his country without completing it, knowing that he did not stipulate a condition at the time of his intention? And is a fidyah for delay incumbent upon him despite his repeated attempts to pay?

It was not permissible for you to refuse the 'Umrah due to illness, and you were obligated to remain in your state of ihram to complete the rituals. You are still in your state of ihram, and you must refrain from its prohibitions and proceed to Mecca to complete the rituals. If you are unable, then you have the ruling of one who is muhsar (prevented), so you may release yourself with a hady (sacrificial animal). If you cannot find one, then you must fast for ten days. What you committed previously of prohibitions out of ignorance carries no accountability for you. As for your wife, if she stipulated at the time of ihram and then refused her ihram without a valid religious impediment, then she is subject to the same as you: coming to Mecca and completing the rituals. If she is unable to come, she is released, and there is nothing upon her, and her stipulation benefits her. However, the stipulation is only beneficial if a hindrance prevents the muhrim from completing the rituals.