What is the Islamic ruling on manufacturing and fitting teeth? Is this considered a resemblance to Allah's creation? Is orthodontics considered a change to Allah's creation?

The fundamental principle is to prevent altering Allah's creation. This is supported by the Quran's prohibition of alteration and the Prophet's (peace be upon him) curse upon those who pluck eyebrows (al-mutanammisat) and those who create spaces between their teeth (al-mutafallijat) who change Allah's creation.

Certain cases are exempted due to necessity or a religiously recognized need. Examples include the installation of artificial teeth when needed for chewing food or correcting speech. This is supported by the story of Arfajah ibn As'ad (may Allah be pleased with him) when the Prophet (peace be upon him) commanded him to use a nose made of gold in place of his severed nose.

As for orthodontic treatment (teeth straightening), if it is due to a deformity or defect, there is no harm in it to remove this defect. However, if its sole purpose is to increase beautification, then it is forbidden.