What is the ruling for someone who entered into a state of Ihram for 'Umrah without a condition, then was forced to leave his state of Ihram due to an accident, and then completed the 'Umrah by entering into a new state of Ihram from Al-Tan'im? And is it sufficient for him to fast three days as expiation?

It was obligatory to remain in the clothes of Ihrām to complete the 'Umrah (definition). Since you did this out of ignorance, there is nothing upon you, and your second Ihrām is not considered. If you committed a forbidden act, such as clipping nails, cutting hair, or hunting, then you must offer a ransom (fidyah (definition)), because the obligation of fidyah for these destructive acts is the same for both the knowledgeable and the ignorant. You must offer a fidyah for each type of act. The fidyah is one of three options: slaughtering a sheep in the Haram (definition) and distributing its meat to its poor, or feeding six needy people (half a Sa' for each needy person), or fasting three days.