Is it permissible to go for Umrah while having unfulfilled fast days from Ramadan, and is it obligatory to make them up before Umrah, or is it permissible to do so after returning from it?

There is no necessary connection between performing Umrah (definition) and making up missed days of Ramadan (definition). Therefore, it is permissible for someone who has missed fasts to perform Umrah, and there is no known disagreement on this matter. However, missed Ramadan fasts must be made up before the entry of the subsequent Ramadan, and it is more virtuous to hasten in making them up. If the breaking of the fast was due to a valid excuse, then the making up can be done at leisure, as long as the next Ramadan has not begun. But if it was without a valid excuse, then making them up must be done immediately, according to the preponderant opinion. Nevertheless, delaying the making up of fasts does not affect the validity of the Umrah.