Regarding focus - are you using tap to focus? I have not noticed slow focus or lag at all, but I do generally tap to focus. I suppose the software that tries to determine what to focus on could be weak and that may be causing your problems and why I have not seen those problems.
Action shots- eh, not sure really as I find the whole form factor and ergonomics of phones not really conducive to good action shots so I really don't bother with them and when I do and get bad shots, I blame my technique and poor handling of the phone for the biggest part of any disappointment. I would really be surprised if any phone camera is consistently taking great action shots.
Regarding video - I find it to be pretty good, but I do try to use good technique and hold the phone steady while making a video. It could be that if you are not using good technique the OIS system can't keep up.
The audio may be mediocre, as in average, but it certainly isn't bad.