What is the ruling on a wife checking her husband's private matters to verify the existence of other female relationships? And what is the ruling on a husband leaving his wife without intimacy for a long time while they live in the same house?

It is not permissible for a wife to search for her husband's private affairs with the intention of uncovering his female relationships, as this constitutes spying and suspicion, which are forbidden by Islamic law. If she ascertains the existence of sinful relationships, she must advise him and remind him of Allah. It is not permissible for a husband to leave his wife without conjugal relations for a period that harms her, as this contradicts living together in kindness.