Is ghusl obligatory after inserting the right hand into the toilet bowl to clean it, or is it sufficient to wash the hand with water and soap then perform wudu, and is prayer acceptable in this case?

If a person's body or clothes are afflicted with ritual impurity (najāsa) while they are in a state of ablution (wuḍūʾ), their ablution is not invalidated by that. This is because none of the nullifiers of ablution have occurred. They are only required to wash the impurity from their body or clothes, and then they can pray with their existing ablution. It is preferable to remove the impurity with the left hand. If there is a need to touch impure water, it is better to wear a glove. If a glove is not available, then the touch should be with the left hand, not the right.