I can confirm number one, that's on legacy design for me. A number of visual glitches involving units when they are selected and especially when given orders.
As for the battles, I think those are too situational to consider the update to be causal. The bombers flying out for a tick where nothing winds up happening at all for example has happened to me many times over the years.
A thing I did notice though is that damage efficiency appears to play a bigger role in battle calculations now, but not just since the most recent update. A single infantry unit appears to have a really dang good chance of holding its own against anything up to 12 attacking units for at least a tick. It's also observable in larger battles how a higher damage efficiency seems to give you a massive advantage now. I personally think it's overdone and could be tuned back a notch.