Is it permissible for a person who broke fasting in Ramadan because of being sick to pay a ransom?

If there is hope for him/her to be cured, then he would be required to make up for the missed fasting days when he/she recovers, and no ransom is due on him/her. If his/her disease is incurable, then he/she would be required to pay a ransom for each missed fasting day, which is (600) grams of wheat, or rice. And Allah Knows Best.

Is Zakah (obligatory charity) obligatory on indebted merchant?

Debt doesn`t abrogate the dueness of Zakah, thus a debtor who has money, articles of merchandise, or other Zakah funds at his disposal should pay their Zakah.

Is it permissible for a menstruating woman to recite the Quran from the computer without actually touching the Quran?

It is not permissible for a woman in her menstrual period, or in postpartum to recite the Quran, even by heart, or without actually touching the Quran itself. Recitation itself is what is prohibited on her regardless of how it is done. However, it is permissible for her to surf through the Quran by her eyes, or to recall it in her head without uttering the words. There is no harm for her to look at the Quranic verses on the computer without touching it, or to utter the words as this is called looking not reciting or reading.

I see horrible dreams although I perform the prescribed prayers, what do you make of that?

All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

Be mindful of Allah while awake and he will safeguard you from whatever evil you see while asleep. We advise you to make the pre-sleep supplications. And Allah The Almighty Knows Best.