Must I offer a sacrifice or not, after the first ‘Umrah’s tahallul with a razor, then entering into ihram for a second ‘Umrah from Al-Tan‘eem and performing its tahallul by clipping nails without shaving, then, 7 months later, cutting my hair with the intention of performing tahallul from the second ‘Umrah?

If the pilgrim in ihram has no hair on his head, he is released from the 'Umrah immediately upon completing the Sa'i. Shaving or shortening the hair is not obligatory for him. It is only recommended for him to pass a razor over his head, and there is no fidyah (expiation) upon him. The majority of scholars hold this opinion. As for clipping nails, it is among the prohibitions of ihram.