I sometimes have to press the turn button twice to end the turn. It only happens when I have units set with move orders that last more than a single turn. The first time I end turn performs these queued moves. The second time actually ends the turn. I'm not sure but this may be what you are seeing.
I've not seen your second bug happen. Did it happen just once, or are you able to reproduce it?
I know what you mean, but this wasn't the case here. My army did not have move orders and did/would not move at all until the second press of the turn button. All AI units would move on each press of the turn though, giving the computer two turns to my one.
The pike unit that would actually grew with damage taken I only seen this once before switching the game down in disgust.
I mean these are only a couple of obvious bugs, the whole game feels like it's built on flaky code. Things are happening that don't feel right or have unusual results, such as going into a battle with bandits and finding it a band of ogres, which quickly change back to said bandits.
I guess I should not have opted in for a beta build, it seems to break more than it fixes.