Is it a condition for the pilgrim (mutamir) to have the financial ability to perform Umrah, or is it permissible for another person to donate the expenses of Umrah for the needy?

It is permissible for a person to donate money to someone performing Umrah, and he will be rewarded for it. It is not a condition for the validity of Umrah that it be performed with the pilgrim's own money or that he possesses financial capability.