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.
What is the ruling on a person who isn`t able to fast due to old age, or an incurable disease?
Paying the ransom is due on such a person, and that is giving a Mud (600 grams) of wheat, or rice, or the price of that amount to a needy Muslim for each missed fasting day. And Allah Knows Best.
Is a Muslim is Permitted to Pray Wearing Shoes?
All perfect praise be to Allah The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions There is no harm for a Muslim to pray wearing shoes or slippers so long as they are pure, since a man asked Anas Ibn Malik: "Did the Prophet (PBUH) use to offer the prayers with his shoes on?" He said: "Yes." Moreover, Ibn Rajab (May Allah have mercy on his soul) said: "Performing prayer wearing slippers/shoes is permissible according the majority of the Muslim scholars." [Fatih Al-Bary,vol.2/pp.274]. And Allah Knows Best.
Which is better, to pray at a prayer place (Musala) whereas many people pray in it, or at a near by mosque in which a few people perform prayer?
Praying at the mosque that has a bigger number is better so long as the number of praying people at the other mosque permits performing prayers in congregation. And Allah Knows Best.