There are some life threatening diseases about which, doctors predict the possible time of death with 99% accuracy. It is because the disease is very dangerous and there is no treatment. Common examples are cancers which already spread to all body (metastasis) or full blown AIDS etc. Doctors usually advise the patient to accept it and to do all things what they want to do for their children or themselves before death. In such cases how a Muslim should react?
1)Can he/she still believe that a miracle could happen? I saw many cases in which usually patient died within the time period (more or less) given especially in metastasis cancers.
2)If he/she accepts that he/she soon going to die, according to latest science research,. and tries to arrange something for his kids or family before dying would it be sin?
3)Would it mean "NOT TRUSTING GOD IN SAVING HIS/HER LIFE"?
4)If he/she would become good Muslim in practice after knowing about his short life Allah would accept his/her good (deeds) after knowing that he/she is soon going to die?
5)What is the best du'a (prayer) he should make during this time?
Every human being dies, to know when (even an approximation of when) from a perspective is actually a blessing.
I don't think it is about miracle. I think it is about believing that God keeps people alive as long as it is written for them and then take their souls as soon as it is written for them. A religious person should believe that despite the illness and its signs and all the predictions of the doctors, if God does not want him to die, he will not die. Just as it is also a religious belief that no matter how safe, healthy and protected one might be, if God wants to take his soul, He will.
We are bound to do things in accordance to the information we have and what rationality tells us while trusting God and believing that everything is in His hand and that He can easily change the course of events if He so desires. Therefore doing good things in fear of leaving this world soon will not be against trusting God.
There is no reason why God might not accept the good deeds of a person who thinks will shortly die. This is different from the case of a person who delays his repenting from sin till his death. Of course there is nothing better than always doing good and saving for our hereafter and being conscious that our death might be very close.
Dua is a matter between God and His servants and no one knows better what he has to say to his Lord better than the person himself. I think praying for becoming cured, along with asking God for forgiveness and for protection of what we leave behind (in case His wisdom was that the person should die from the decease).