I couldn't find a real solution for the Chrome issue, but "fixed" it with the help of browser sniffing. (Not ideal, I know. Any help welcome.)
Regarding my second issue, this is due to my removing most of window_resize() here: https://github.com/splitbrain/dokuwiki/commit/48c5eff7672d7e6fcfc3f64194e03253d8e2fd0f
My adding it back in (and adjusting it accordingly) doesn't make it much better. So, I'm inclined of not fixing it (at least not that way). Maybe we could instead reset the widths in the case of window resizing? Not perfect either, but a better solution than the current or the old one IMO.