Do certain vaginal discharges and incontinence of urine nullify ablution, and should underwear be changed?
A person afflicted with constant impurity due to urinary incontinence and vaginal discharges is obliged to make ablution for every obligatory prayer when its time is due, and after removing Najaasah (impurity), and wearing a clean diaper. He/she is obliged to pray immediately even if the impurity is being released, and he/she is obliged to remake ablution, and the aforementioned for every obligatory prayer.
Is it permissible for the man to go out wearing shorts?
All Perfect Praise is due to Allah, The Lord of The Worlds
It is permissible so long as his Awrah (private part), which is between his navel and knee, is covered. However, the regular wear traditions and modesty are to be observed. And Allah Knows Best
Is the Saum (Fasting) of someone who ate and drank forgetfully while offering fasting of oath expiation invalidated?
Whosoever eats, or drinks forgetfully is exempted by Allah; therefore, he/she shouldn`t break their fast whether it was obligatory, non-obligatory, or expiatory. And Allah Knows Best.
What is the ruling on making a false oath?
Making false oath indulges its maker in Hell; therefore, he is obliged to repent, ask Allah for forgiveness and make an expiation; feeding 10 poor or providing clothes for them and in case of incapability of doing any of latters he should fast for 3 consecutive days. And Allah Knows Best.