Is it permissible for a religious young Muslim woman to love a young man for Allah`s sakes?
Such love between the two sexes is from the devil`s evil suggestions, and a pure Muslim woman should beware of such a matter, and she shouldn`t mix with non-Mahrams (Marriageable ).
Is it obligatory for a wife who has been abandoned for many years to observe the waiting period (iddah) after her husband passes away?
If her husband passes away, the wife is required to observe the waiting period (Iddah), even if he had abandoned her, because she is his wife and inherits from him, so she must observe the iddah after his death. And Allah Knows Best.
Is it permissible for a person to sever ties with his sister because her husband had quit prayer and done him harm?
A sister is a blood-relative and maintaining blood-relations is obligatory in Islam. As regards her husband, he should be invited to the way of Allah with wisdom and beautiful preaching.
What should one who forgot to offer the second Sajda during congregational prayer, and remembered it before the end of the prayer do?
All perfect praise be to Allah, The Lord of The Worlds. Whoever forgets a pillar of prayer while in congregation must follow the lead of the Imam, and after the latter offers Tasleem, he should offer one Rakah, then perform Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.