Is hair extension permissible?

All Perfect Praise is due to Allah, The Lord of The Worlds 

It is impermissible for the man and the woman to apply a human`s hair as extension, but using artificial hair is permissible for the married woman after obtaining the approval of her husband, and provided that non-Mahrams (Marriageable men) don`t see her. And Allah Knows Best.

Is the patient who is on dialysis twice a week obliged to observe fasting? Is his fasting on the days he is on dialysis considered valid or not?

Praise be to Allah the Lord of the Worlds.

Dialysis invalidates fasting because of the nutritional fluid used in that procedure, as pointed by specialized doctors, in addition to causing bodies to enter the stomach. Therefore, it is recommended that the patient who had undergone dialysis to observe fasting for the rest of that day, if he is able to, and make up for it after Ramadan. However, if the doctor told him that fasting, at any time, would damage his health, then he must break his fast and pay a ransom against every missed day. We pray that Allah blesses this person with recovery. And Allah The Almighty Knows Best.

Is it permissible for me to make up for my late father`s missed fasts, and should I make an intention to this end by saying: “I intend to make up for my late father`s missed fasts .”

It is permissible to fast on behalf of the deceased father in order to make up for his missed fasts, and you should make the intention for offering fast from night time, but uttering the intention isn`t a condition.

How is the Zakah(obligatory charity) on articles of merchandise calculated?

(2.5%) of each article`s value is paid as Zakah after a whole lunar year had lapsed.