Is it permissible for me to perform 'Umrah for myself after performing 'Umrah on behalf of the person who commissioned it? And is it permissible for me to save some of the money given to me by the person who commissioned it for food and drink?

It is permissible for you to perform Umrah on behalf of another, so long as you have already performed Umrah for yourself. It is also permissible to take payment for performing Umrah on behalf of another. If the Umrah is performed for a specific amount as wages, then whatever remains after your expenses is yours. However, if it is performed in exchange for expenses such as outlays, accommodation, and travel tickets, then any surplus must be returned to the one who bore those expenses. If a person is given money for Hajj and told, "Perform Hajj with this," he may be expansive in its use, and whatever remains is his. But if he is hired to perform Hajj, then what he takes possession of and disposes of is his, and whatever remains is his. However, if he is given money to cover the expenses of Hajj according to what is customary, he must return any surplus.