Is the Umrah I performed on behalf of my deceased mother valid, given that I entered into a state of ihram and found a small amount of red color on my underwear, which I did not consider menstrual blood because it was not my usual time for menstruation, but it later became clear that it was menstrual blood that had come earlier than its usual time?

May Allah have mercy on your father and all deceased Muslims. Your 'Umrah is valid, and there is nothing upon you, because the default state is purity. What you found on your underwear does not necessarily have to be menstrual blood, especially since it was not at its usual time. Doubting the impediment is baseless, and this is supported by the Prophet's (peace be upon him) saying: "He should not leave [his prayer] until he hears a sound or finds a smell." However, if you are certain that it was menstrual blood, then refer to fatwas numbered 147845 and 120425.