You can also think of it as a phrygian scale with a raised third. I think that it is just as important to understand what about a scale/mode is characteristic and how to construct one. Basically, learning the "formulas" for the scales and modes. For instance rather than try to think that E Phrygian Dominant is the 5th mode of an A harmonic minor scale (which it is), then find the notes of an A melodic minor scale, then start on E, etc. I find that if you know that the formula for a Phrygian Dominant scale is built as a phrygian scale with a raised third, you can simply start on E and build accordingly E, F (lowered 2nd for phrygian), G# (raised third), A, B, C, D, E.
It also helps to learn the formula in terms of the intervals between scale degrees. In the case of phrygian dominant you have a half step, 1.5 steps, half, whole, half, whole, whole.
To answer your question about "true" arabic scales, Ravi Shankar and the music he played was not arabic at all. Ravi Shankar played Hindustani music. And yes some of their "scales" (because thay aren't exactly comparable to western scales) contain intervals smaller than a half step. However, to our western ears, the phrygian dominant scale does sound "arabic."