Not being a historian of the 14th through 16th century Middle East, I can't speak to the Moorish or Turkish or Mamluke reaction to plate armour. Perhaps one of any Ottoman/Mamluk/Moorish historians can help with this. I also cannot say definitively that the Ottomans, Manluks or Moors did not use full plate armour, though I am not aware of any examples other than some 15th century sallets that may be Moorish.

Regarding the second part of your question, this is a very difficult question. It is hard enough to explain why something -did- happen in one time or place. Trying to describe why it -didn't- happen in another is often even harder. This is because it requires two complete sets of knowledge - all the factors that led to a historical event or development in once place or time, and the way in which they were lacking in some other place or time when it -didn't- happen. To a certain extent this applies to the question of adopting technologies - even if something is developed in one place that has contact with another, this doesn't mean that the technology will be adopted - it might just not make sense in the other historical context. We are used to thinking of technologies as 'better' than other technologies, but sometimes they are different tools for different tasks.

In many ways, it is perhaps more illuminating to see plate armour as a great exception to most iron or steel armour in history, which is made of mail or smaller plates. Rather than assuming that plate armour is the natural development of armour, we can look at it as a unique development from a particular time and place. I try to explain in this answer -some- of the factors that allowed for and led to the adoption of plate armour in Europe. It is not an explanation of why it wasn't adopted in other regions, since I cannot speak to the metallurgical traditions, social organization and 'way of war' of societies outside of Europe.