Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
Is a woman sinful if she fasts out of shyness from her family while menstruating or in postnatal bleeding?
It is forbidden for a woman who is menstruating or in postnatal bleeding to abstain from food and drink with the intention of fasting. If she fasts out of shyness, she is sinful, as her fast is not valid.
However, if she refrains from eating and drinking without intending to fast, it is not forbidden, but she unnecessarily burdens herself without need.
What is the ruling on swimming while fasting?
Swimming while fasting is disliked (makruh) due to the risk of water entering the body cavity (jauf) through the nose, ears, or mouth, which would break the fast.
Ramadan is a month of tasbeeh (glorifying Allah), not Sibaha (swimming).
Does collecting saliva and swallowing it break the fast?
Swallowing collected saliva does not break the fast, but it is an unnecessary and meaningless act.