The Beyneu - Kungrad road is definitely not well travelled, but doable, although the road is very bad.
You cannot enter and leave Turkmenistan from/to the same country on a transit visa - you need to go through Turkmenistan, for instance from Kazakhstan to Uzbekistan, or from Uz to Iran. You will need both visas in advance before you apply for the Turkmen transit visa. Istanbul or Ankara are possibilities for all your stan visas. See the embassy reports on the previous link for more on that.
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