Assalaamu alaykum, Shaykh. I am a 15-year-old who is currently doing Da‘wah (proselytization), and I just want to verify some information that I have given someone. This is with respect to the following questions: Does God have the power to create a stone which He can not carry? Does He have the power to be unjust? Does He have the power to lie, or can He lie if he wants to?" The same goes for questions which are similar to the above.
This is what I said: All our scholars (Ahl-us-Sunnah wa-l-Jamaa‘ah), without exception, believe that Allaah's power is not connected to irrationalities, and He has the power to do all things, but it does not include impossibilities. Therefore, it is not right to say that Allaah has the power to lie or can tell a lie if He wants to.
Did I answer the question correctly? Please, Shaykh, I beg you in Allaah's name to answer my question specifically, without referring me to some other question in your website. You would be doing me a huge favor. May Allaah reward you.

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

First of all, we would like to give you an educational answer before giving you a scientific answer. We advise you to not engage in debate with those who ask you those questions, especially given that you are very young and that it is most likely that you are not firmly grounded in Islamic knowledge.

You should know that the Companions did not ask the Prophet such questions as 'Does Allah have the power to create a rock that He cannot carry?' and the same goes other such nonsense, which is in fact inspired by the devil and which he whispers in the hearts of his allies to argue with the believers; as Allah, The Exalted, says (what means): {…And indeed do the devils inspire their allies (among men) to dispute with you.} [Quran 6:121]

Ash-Shawkaani wrote in Fat-h-ul-Qadeer, “And indeed do the devils inspire their allies (among men); meaning that they whisper to them with whispers that are contradictory to the truth; and their intention in doing so is that those allies argue with you with that which the devils whisper to them…”

Those questions do not come from a heart that is filled with the glorification of Allah; rather, they come from the whispers of Satan (the devil) and his attempts to deceive people. Getting carried away with these questions is getting carried away with the whispers of the devil. Indeed, the Prophet informed us about people getting carried away with the questions of Satan.

Anas ibn Maalik, may Allah be pleased with him, narrated that the Prophet said, “People will not stop asking questions till they say, 'This is Allah, the Creator of everything, then who created Allah?’” [Al-Bukhaari and Muslim]

The version of the hadeeth reported in Saheeh Muslim reads, “Allah, The Almighty, said, ‘Verily, your nation (Muslims) will continue to ask about this and that until they will say, 'Well, it is Allah Who created the creation, but who created Allah?'’”

The Prophet ordered us to stop asking these questions and stop thinking about them. Abu Hurayrah, may Allah be pleased with him, reported that the Prophet said, “Satan comes to one of you and says, ‘Who created such-and-such?’ until he says, ‘Who created your Lord?’ If you reach this extent, seek refuge with Allah and put an end to such thoughts.” [Al-Bukhaari and Muslim]

Ibn Hajar wrote in Fat-h-ul-Baari, “A person must seek refuge in Allah and stop, meaning that one is to stop being carried away with the whispers of the devil; rather, he should turn to Allah in repelling him. He should know that the devil wants to spoil his religion and his mind with this Waswaas (obsessive whispering); so he should strive to repel them by engaging himself in something else.”

Lastly, in regard to your saying that the power of Allah does not include impossibilities, Shaykh Ibn Taymiyyah said:

“A group of scholars said: injustice is possible, and Allah is able to do it, but it is not befitting of Him due to His justice. Allah praised Himself by informing us that He does not wrong the people in the least. Praise is for refraining from doing what He is able to do, not for refraining from what He cannot do … This is the view of most scholars of Ahl-us-Sunnah, and the scholars who affirm Qadar (predestination) among the scholars of Hadeeth, Tafseer (interpretation of the Quran), Fiqh, theology, as well as the Sufis who follow the four Schools of jurisprudence and others.”

Allah knows best.