Is prayer obligatory for one who experienced a small amount of menstrual bleeding before Maghrib and it did not stop until 'Ishaa, while feeling menstrual pain and her usual period not having ended?

Yes, your fast is valid. A drop of blood is not considered menses, because menses is blood that flows from the womb. Sheikh Ibn Uthaymeen was asked about a small drop of blood appearing during Ramadan, and he replied that her fast is valid, and that these drops are not menses because they come from the veins. He also narrated from Ali ibn Abi Talib, may Allah be pleased with him, that drops resembling a nosebleed are not menses.