Before he spent some time in Transnistria as well, which is also a weird choice.

Maybe not. If you claim to be living in an active warzone and go missing who would look for you?

Flee to Western Europe under an assumed identity, get taken in as a refugee?

They ruled it was tried in the wrong jurisdiction thus basically never happened. There is likely a sealed indictment awaiting in another jurisdiction where they will try again, now knowing the trial strategy of the defense.

Overturning a conviction is usually permanent, however, that does not necessarily mean the verdict becomes Not Guilty, and only when the verdict is Not Guilty does double jeopardy come into play. It is possible for a higher court to overturn a lower courts decision, have it returned for reconsideration, or even a whole retrial. In other cases a higher court will overturn a verdict and instruct the lower court the change the verdict to Not Guilty.