Should the Had punishment for adultery be carried out on a pregnant woman after she confesses to it, and was the condition for carrying out this punishment on her the presence of four witnesses? And why did the Prophet (peace be upon him) not order her to repent?

Adultery is proven by evidence (the testimony of four witnesses) and by confession, as happened with the woman from Juhaynah who confessed to adultery, and the Prophet, peace and blessings be upon him, stoned her. That woman confessed to the حد (prescribed punishment) for adultery so that the حد would be carried out upon her. If the حد is brought before the ruler and proven, there is no pardon, no annulment, and no intercession in it, and it must be carried out. And it is obligatory for the Imam to carry out the حد if its matter becomes manifest.