What is the fate of the Umrah, and is a make-up (qada’) required, if a woman performed Umrah after purifying from menstruation, then intermittent brownish blood descended from her, which was later found to be pregnancy blood?

Your 'umrah is valid because the blood you saw is not menstruation, for a pregnant woman does not menstruate according to our view. Nor is it nifas (postpartum bleeding) because there was no discernible human creation in the miscarriage. Thus, it is dam fasad (irregular bleeding/istihada), and circumambulation (tawaf) with its presence is valid. Your ghusl (ritual bath) after it was obligatory. Ibn 'Umar issued a fatwa to a woman who experienced something similar, advising her to perform ghusl, bind herself, and perform tawaf.