Answer
(Fatwa: 782/1030=H/1429)
(1) If the widow of late Majid is neither a syed (the family of the Prophet peace be upon him) nor owner of Nisab (amount prescribed for zakah), then giving Zakah to her is correct. She can possess it and spend it on her children.
(2) Women also belong to caste. If her father is from syed family, she will also be Syedah, but in this situation, she will not entitled to receive Zakah. You might be in doubt on lineage. Actually, lineage belongs to father not to mother.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband