Is it permissible to obligate a Muslim to perform the Fajr prayer half an hour after the Adhan based on the Almighty’s saying: "until the white thread of dawn becomes distinct to you from the black thread [of night]," and on the Hadith about the two dawns? And does performing the prayer immediately after the Adhan invalidate it?

No one is allowed to compel another to accept their opinion on matters of differing views, such as the issue of when Fajr begins. It is incumbent upon a Muslim not to pray unless they are certain or have a strong presumption that the time for prayer has begun. Whoever knows the signs of the time entering and has a strong presumption of it, let them pray, and no one should prevent them. As for whoever does not know, let them follow someone they trust. It is permissible to follow reliable calendars. We have explained that the Umm al-Qura calendar can be relied upon, with a delay of a few minutes for Fajr prayer beyond what it indicates, as Sheikh Ibn 'Uthaymin pointed out.