Is there a specific way to perform the Tahajjud prayer, such as it being eleven or twelve rak'ahs, in which Surat Al-Ikhlas is recited twelve times in the first rak'ah, and then the number of its recitations decreases until it is recited once in the last rak'ah?

There is no specific method for Tahajjud prayer or night prayer. The Muslim prays two rak'ahs by two rak'ahs, reciting whatever is easy for him from the Qur'an, then prays Witr.

Praying Tahajjud with eleven or twelve rak'ahs, where Surah Al-Ikhlas is recited twelve times in the first rak'ah, then the number of recitations decreases until it reaches one time in the last rak'ah, is an innovated bid'ah and contrary to the Sunnah.

Night prayer is two by two. If one fears the dawn, he prays Witr with one rak'ah. Most of the Prophet's (peace be upon him) prayers were eleven rak'ahs. There is no harm in increasing or decreasing.

There are no specific surahs from the Qur'an to be recited in night prayer; rather, one recites whatever is easy for him from the Qur'an.

Qiyam al-Layl (night vigil) is a confirmed Sunnah, and its last third is the best. One prays two by two and concludes with one Witr rak'ah, reciting whatever is easy from the Qur'an.