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 to make up for missed fast after the beginning of the second half of the month of Sha`ban (the month before Ramadan)?

Yes, it is permissible, but one who had missed fasts should hasten to make up for them. As for the Hadith mentioned in this regard, the prohibition is for offering absolute voluntary fasting. And Allah Knows Best.

Is it permissible for a person, who vowed to offer two Rak`ahs (units of prayer) everyday for Allah`s sake, to do so after the Fajr (dawn) prayer?

In principle, a vow should be fulfilled as it was originally intended, and if its time lapses then, it should be fulfilled at any time because of the vow. Therefore, it is permissible to offer them after the Fajr prayer, and there is no prohibition in doing so. However, it is preferable for him to offer these two Rak`ahs at some other time to avoid the disagreement amongst the scholars in this regard.

Is permissible to abort my embryo if there was a risk on my Life?

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                                                                                                                                                                                                                            Abortion is permissible if it was confirmed that the existence of the fetus within his mother's Belly might cause her certain death.Therefore, abortion is permissible if the above conditions were met. And Allah Knows Best.