Alright! This'll be a short version. I should write this down somewhere; I have answered very similar questions before, but have lost the answers.
First: Why are you fascinated by conlangs in general and Dothraki/Valyrian in particular?
Language is a fascinating thing in general. Conlangs are innovative, sadboxy, artistic and safely concise worlds. A lot of things are in sharp focus, clear and inclusive. You can go far with relatively innocent dip of a toe and there is no confusion, internal or external, that you are doing something with straightforwardly applicative goal.
Dothraki (and Valyrian, too) plays an important and interesting role in the joyrney of both fantasy genre and conlanging scene. Dothraki is also real nice in that it's quite rough and tumble, Dothraki as people are not role model material and their culture is illiterate monoculture, nothing fancy. That offers a limited scope and a kind of a layer anthropologic realism (the latter part can be argued - Dothraki can easily be seen as cardboard thin archetype badass barbarians, I just see that more as a challenge and freedom than an end of the conversation).
Second: What is your motivation for learningDothraki/Valyrian?
Well, it was largely the fascination with conlangs and Dothraki, which motivated me. See the former answer.
Dothraki was there at right time for me. I had mental space and time for it and it was green and hip. And I had a bit of a relationship with ASoIaF (and fantasy in general) that needed some kindling.
The circle of interested people was small enough that it did not scare me away, but quite the opposite, it made me feel I was, after a fashion, doing something worthwhile.
Third: To what extent do you think that the language Dothraki reflects the martial character or other character traits of the Dothraki people?
Well, I think mr. Peterson has kept it quite realistic, has not gone overboard. There's certainly a lot of resonance, but not everything is dictated by the cultural attitude, there's randomness and legacy stuff as should be expected.
Actually I don't consider DJP particulary superhuman. He's probably done much better work from linguistic perspective than from anthropologic perspective, but the work is in no way unimpressive in any account. Peterson has also kept writing the culture at reasonable minimum, trying to build only on what has been established by GRRM and GoT producers. We don't have the whole created language, and what has been created has it's limits. So on some part of the hypothetical whole of the language, jury is still out.
