Is it correct that it is not possible for Allah to do the following:-create another God-lie or sin or oppress-adopt a son-make a rock that he cannot lift (because that is similar to asking, Can Allah be deficient)?

All perfect praise be to Allah, The Lord of the Worlds. I testify that none is worthy of worship except Allah and that Muhammad is His slave and messenger.

It is intuitively known that ability is only relevant to the realm of the conceivable and possible rather than that of the inconceivable and impossible. Verily, Allah The Exalted is Competent over all things; however, what is impossible or inconceivable is non-existent to begin with, so, it cannot be related to the Ability of Allah and His Will.

The first and last examples mentioned in the question (the creation of another god and creating a stone that cannot be carried) fall into this category: the impossible and inconceivable. Likewise is the issue of adoption if it is intended to mean reproduction. But if it is intended to mean that Allah may choose any of His Slaves, then this is not impossible according to reason; yet, it is impossible according to the Sharee’ah; Allah The Exalted Says (what means): {If Allah had intended to take a son, He could have chosen from what He creates whatever He willed. Exalted is He; He is Allah, the One, the Prevailing.} [Quran 39:4] Abu Hayyaan commented on the verse saying, “{If Allah had intended to take a son...}: this denotes honoring and adopting him, as it is impossible that it denotes having a son through the known reproduction process, which is inconceivable in relation to Allah The Exalted. {He could have chosen} means He could have selected from His creation whom He wills to be an adopted son. But He, Exalted may He be, never willed so, as He Says (what means): {And it is not appropriate for the Most Merciful that He should take a son.} [Quran 19:92]…” [Al-Bahr Al-Muheet]

The same is true with regards to the issue of injustice and any similar flaw. Although they are conceivable based on reason, they are impossible as per the Sharee’ah. Indeed, Allah is Exalted above any aspect of imperfection and is far above all shortcomings and flaws.

Allah Knows best.