Is it permissible for one to masturbate in order not to commit fornication?

This is called committing the milder of the two evils such as eating a carcass in fear of death, and this happens when committing fornication is very likely to occur.

Is it permissible for us to sever ties of kinship if our blood-relatives` gatherings involve acts of sin?

Maintaining kinship ties is mandatory, thus if visiting your blood-relatives hinders their sinful acts , then you should do so. However, if their sinful acts persist while you are at their gathering, then it is sufficient that you maintain kinship ties via telephone and the like.

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.

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.