I am doing a research on Islamic law and I need a clarification on some of the following isues: First: Does the principle of gradual implementation of sharia also apply in cases like theft? Can the leader apply another punishment until his people is well educated islamicly? Second: What is the punishment in cases where retaliation is forbidden,like when a parent kills his child or when a muslim kills a non-muslim? Third: Is the book qawaid al ahkam reliable in the field of law? I heard some scholars praising it and others condemn it.

All praise be to Allah, and may His peace and blessings be on His last and best messenger, Muhammad and his purified household and honorable companions.
As for the issue of gradual implementation of shari’a, it is of the more complex matters to address and must be tackled by the grandest and most trustworthy scholars of Islam so as not to become an excuse for abandoning the shari’a. but, generally speaking the gradual implementation of shari’a is acceptable given there will be no unwarranted delay or deferment of its application in entirety, which is a collective obligation on the ummah.
As for the parent and child and the Muslim and non-Muslim, the punishment will be decreed by the judge to suit the crime. There are disagreements over these rulings between the scholars, and some indicate that if the parent’s killing of the child is known to be intentional and premeditated, then they are killed. The disagreement regarding the Muslim and non-Muslims could be sought in the fiqh books.
As for the book Qawa’ed al-Ahkam by Imam al-‘Ezz, it is one of the greatest books written, yet it must be learned under the supervision and guidance of a true scholar so that one doesn’t get misguided by misinterpreting it. After all, it is about the making of fiqh and objectives of shari’a. One may not perform surgery after reading a book on surgery. Allah knows best.