Is a woman`s neck an Awrah (private part)?
All Perfect Praise is due to The Lord of The Worlds.
It is an Awrah, and it is forbidden for her to reveal it before non-Mahrams (Marriageable men). And Allah Knows Best.
What is the ruling on a young man and a young woman having a love relation for the purpose of getting married?
It is forbidden for a man and a woman to have any kind of relation whether for marriage, or not because it leads to committing sin. Such relations include: private meetings, mixing, gazing, and seclusion (Khulwa). Accordingly, one who is sincere in his intentions should go to the woman`s guardian and ask for her hand in marriage.
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 sick person to pray while sitting on a chair?
All perfect praise be to Allah, The Lord of the Worlds It is permissible for a sick person, who is unable to stand up, to offer prayer while sitting on a chair. If he/she was unable to prostrate while on the chair, the he/she should pray while sitting on the ground, but if he/she was neither able to bow (Roku),nor to prostrate, then he can do them while sitting on the chair. And Allah Knows Best.