Q 1:
What is the ruling on a woman marrying a man who was engaged to her daughter for a duration of five months? The engagement was broken by him before the marriage contract was concluded due to a disagreement.
A:
If the situation is as you mentioned, that a man became engaged to a girl, (Part No. 18; Page No. 382) but broke the engagement before concluding the marriage contract, he may marry her mother, as prohibition of this marriage occurs only when the marriage contract is concluded with her daughter, according to Allah's statement,
Forbidden to you (for marriage) are: your mothers, your daughters
until His saying,
...your wives’ mothers
This girl did not become his wife simply by being engaged to him. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.