Graphics software made their own chose regarding to the axis orientation of the 3D world they offer.
Here is a synthesis of these choices.
(article still in development)
Direct: Folows the rule of right hand: thumb is X, index is Y and middle finger is Z
Indirect: Same are Direct but with the left hand: thumb is X, index is Y and middle finger is Z
Tangent Space Normal Map Style:
A description of the common tangent space normal map conventions is presented on this page.
Commonly the UVs origin is at the bottom left corner of the texture (when no offset is applied). In some applications though it can be at the top left, as is the pixels origin of an image.