Hi Angelos,
First I want to congratulate you for talking to non-believers about God and his love for them! I hope you continue on in this work, and I appreciate that you are asking for guidance on how best to give answers to the difficult questions. Keep seeking to save the lost!
One answer that I often tell people is that God cares about our earthly bodies, but he cares even more for our eternal souls. Sometimes, people need to "hit bottom" before they turn to God. If that is what it takes for somebody to turn to Him, as awful and painful as it is for Him to watch that person get to that place, it is worth it to Him if they will turn from their sin and be saved. Many times people's misfortune is a result of their choices, but, sadly, it is often a result of other people's choices (war, abuse, etc.) God is not ok with this, but He works to the good of those who love him.
An example of this happened 2 months ago. My uncle was a strong christian about 15 years ago, but had slipped back into darkness and, in many ways, turned his back on God. My mother prayed that God would intervene in his life to restore the passion he once had for God. The VERY NEXT DAY, my uncle fell knees, hands and stomach, into a campfire, and burned himself so badly his knees were burned down to the cartilage, he needed skin grafts across his stomach and legs, and his hands had no skin left on them (this is bringing tears to my eyes just recalling this tragedy). I am NOT saying that God CAUSED my uncle to fall into that fire, but he certainly used that as an opportunity! As a result of my uncle's misfortune and the excruciating pain and the intense physical therapy and healing process, a network of Christian brothers and sisters offered encouragement and prayer to him everyday through an on-line blog. The prayers went up probably hourly for him, and he has healed almost miraculously in less than 2 months time!! AMEN!!! More importantly than that, though, is that he was so touched by the love that people had for him--many he didn't even know, and the was amazed by the effect of the prayers, that his relationship with the Lord has been restored. AMEN!
God is Love and Love does not delight in evil but rejoices with the truth! Amen!
I hope that helps