What is the ruling on not wearing the hijab while reciting the Quran, performing Tahajjud, praying, and fasting, and do these deeds compensate for not wearing the hijab?

The hijab is an obligation upon women, and the claim that the verses of hijab are specific is incorrect. Abandoning some duties while performing others is not permissible, for Allah Almighty says: "O you who have believed, enter into Islam completely [and perfectly] and do not follow the footsteps of Satan. Indeed, he is to you a clear enemy." The intent is to embrace all the laws and commands of Islam and abandon all its prohibitions, and for a Muslim to do all the good deeds they are able to.