Question: If one missed salats when one was healthy, can one make them up by doing tayammum if one is sick?
Yes, it is permissible. It is permissible to make them up through gestures, too.
Question: Is it permissible to do tayammum in order not to miss Salat al-Jumu’ah?
If one does not have enough time to do wudu’ with water, it is not permissible to do tayammum instead of it in order not to miss Salat al-Jumu’ah because a person who is not able to perform it performs Salat az-Zuhr.
Question: If one who is junub (one who needs ghusl) does tayammum because he cannot find water, does one become junubagain when one’s tayammum breaks?
No, one does not become junub according to the Hanafi Madhhab. But one becomes junub according to the Maliki Madhhab.
Question: Supposing a person is on a piece of open land and the weather is extremely cold. If he knows that he will fall ill if he takes ghusl, what should he do?
If there is the danger that a person, when he takes ghusl, may die or become ill because of cold, he does tayammum for ghusl and wudu’ with water. If he, though he is in a city, does not have enough money to go to a bath and has no other alternative, he does tayammum instead of ghusl and performs wudu’ with water.
Question: Is it permissible to do tayammum for wudu’ or ghusl if there is a danger near water?
If water source is close but there is an enemy, a wild or poisonous animal, a fire or a guard near the water, or if he is imprisoned, or if someone threatens him with death or takes away his possessions if he makes wudu’ with water, he does tayammum instead and performs salat. But since these are caused by creatures, he has to repeat those salats he performed with tayammum after he takes ghusl and does wudu’. If it is not possible to perform them within their specified times, it is necessary to perform them after their times are over. (Radd-ul-mukhtar)