Is it permissible to recite the Quran by way of Al-Tayyibah according to Hafs without having taken it from an authorized shaykh, and is it valid to learn the Quranic recitations from books and written sources without direct reception from authorized shaykhs?

In Tajweed, some aspects are obligatory and some are recommended. There is no harm in shortening or lengthening [sounds] as long as you articulate the letters from their proper articulation points and give them their due. The fundamental principle is to receive the Qur'anic recitation from proficient reciters; it is not sufficient to rely on finding a written text or merely hearing it from a Shaykh's utterance. Rather, it is essential to recite before a proficient Shaykh. It is not a condition for the Shaykh to have an ijazah (certification), but it is sufficient for him to be qualified to teach recitation.