Is it permissible for my wife to perform Tawaf Al-Ifadah and Sa'i using a wheelchair on the second floor, despite her ability to walk, due to overcrowding and limited time to catch the flight? What is the ruling on the appearance of blood-colored discharge after she performs ghusl and returns to our residence?

The wife's circumambulation (tawaf) is valid. There is no harm in her riding while capable of walking, because circumambulating while riding is valid, especially if there is an excuse such as crowding or fear of missing the flight. The evidence for this is that the Prophet (peace and blessings be upon him) circumambulated on a camel, and he ordered Umm Salamah to circumambulate while riding due to an excuse. As for the blood she found after the circumambulation, it is considered menstruation if it occurred during her menstrual period, and she must perform ghusl (ritual bath) after its cessation. Her circumambulation is valid unless she was certain of its presence before or during the circumambulation, because the general principle is that a new event is attributed to the most recent time it could have occurred.