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 prayer mandatory on a dying person who goes through a state of unconsciousness, then wakes up?
If he wakes up and was conscious, then he should pray the way/manner he could, but if he wasn't, then he is exempted from obligatory prayer as Allah Says in this regard (What means): "On no soul doth God Place a burden greater than it can bear." [Al-Baqarah/286].
What should a worshiper who has forgotten a pillar of prayer do?
If he/she remembered the forgotten pillar before offering it in the following Rakah (unit of prayer), then he/she should offer it, and continue the prayer, then offer Sujood As-Sahw (Prostration of forgetfulness) at the end of it. But, if he/she remembered that forgotten pillar after having offered it in the following Rakah, then he/she should offer a new Rakah in its (the one in which he forgot a pillar) place, and offer Sujood As-Sahw.
In life insurance with the Potash Company, enrollment is mandatory, and employees have the right to receive a cash amount from the insurance for surgeries and illnesses while employed by the company. Is the amount given by the insurance in this case permissible (Halal) or prohibited (Haram)?
Since the insurance is compulsory, then what the insurance company pays in return for medical treatment is similar to donation, and I pray to Allah The Almighty that this is lawful even if this service is deducted from your salary in return of it, so in this manner you take back some of the amount you paid in form of above treatment. And Allah Knows Best.