Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
Is it permissible for a person who broke fasting in Ramadan because of being sick to pay a ransom?
If there is hope for him/her to be cured, then he would be required to make up for the missed fasting days when he/she recovers, and no ransom is due on him/her. If his/her disease is incurable, then he/she would be required to pay a ransom for each missed fasting day, which is (600) grams of wheat, or rice. And Allah Knows Best.
What is the ruling on praying behind an undesirable Imam?
It is permissible to pray behind an Imam who is undesirable for committing religious violations, and it is disliked for such an Imam to lead the prayer. Still, If he was undesirable for a personal, or a worldly matter, then such argument doesn’t hold water. And Allah Knows Best.
Should missed Sunnah prayer be made up?
Making up missed voluntary acts of worship is from Sunnah.