Is it permissible to prolong the sound between the lām and the hāʾ in "Allahu Akbar" and "Ashhadu an lā ilāha illallāh," and what is the extent of such prolongation if permissible, and is it permissible to chant the adhan?

The Madd (prolongation) between the Lām and Hā’ in "Allahu Akbar" and "Lā ilāha illā Allah" is a natural Madd, equivalent to one Alif, because there is no cause for Madd (such as a Hamza, Sukūn, or Shaddah). Exceeding this Madd is considered a forbidden لحن (melodic error) and تطريب (excessive melodizing) in the Adhan.

However, if the Muezzin pauses on a silent letter, such as pausing on "Lā ilāha illā Allah," then a long Madd is permissible due to the presence of Sukūn as a cause, and it can extend up to six Alifs.

Excessive singing and melodizing (تغني وتطريب) in the Adhan by adding more melodies is disliked by the majority of scholars. It does not invalidate the Adhan as long as it does not change the meaning. If it changes the meaning, then it is forbidden.