He's being extradited to France, which probably has less bias, but still a bias. I doubt the US will get involved behind the scene in France, because they've phrased their reasoning for the heist as btc-e's users were money laundering, so even if he is found innocent, the US still gets to keep the money and not look bad.

Russia may have a bias, I'm uncertain. I'm not sure how happy Russia was about btc-e. BTC-e may have been in the Ukraine, but Russia implicitly requires neighboring countries to follow Russian law. Did BTC-e break Russian law? I have no idea. But because he is not being extradited to Russia, we'll probably never find out what Russia thinks.

If Putin holds private keys at the end of this transaction, then - yes :)