Hadith is a narration about Mohammad(puh)'s words and actions. They are like "I heard from this man who heard from that man that Prophet Mohammad(puh) said this, or did this". The most ancient hadith books were written 200 years after the death of Mohammad(puh). They are called Kutub al-Sittah, which means "the 6 books". You can find them here. As you see, they were all written by Sunni scholars.
Hadiths are divided into 3 categories:
- Authentic ones: They seem as the most reliable ones.
- Made up ones: They are believed as they have been made up for political reasons etc. They are either against Quran clearly, or their narrators weren't trustworthy.
- Can't decidable ones: They are seem to be fine and accurate, but their narrators are not trustworthy or unknown.
About Quran's and Hadiths' points of view, please look at my answer in this question.
About the Ottomans and Persians, they did painting yes, but not similar to western painting. They either didn't draw the face, or they didn't draw it properly. Please search for miniature. In later period, they abandoned this and draw just like westerners. But somebody's decisions or actions don't change "the theory".
Why are there so few living beings portrayed in Islamic Art?
Because of the hadiths. Please look at the link I gave.
Does it make a difference if it is secular or religious art work, human or animal figures?
Yes. It has been allowed to draw non-living things. This is why Islamic societies draw trees and different geometric shapes through history. Please search for enamelled tile.
It differentiates if you support your claim with different hadiths. According to some, you can't draw anything at all. According to some another, you can't draw living things only. According to another interpretation, you can't draw faces. According to another interpretation, you can't draw properly. The Ottomans usually applied the last one, the Persians on the other had usually applied the 3rd.
Is portrait painting of an identifiable individual allowed?
Every authority in history seem to prohibited it. But in later periods, as I said, they painted like westerners.
The main purpose to prohibit painting and sculpturing was to keep people away from returning to idol worshiping. Some people take this literally and didn't look to the reason, while some other people tried to find a gap in this rule.