Could you say if its possible to externalize screen on av out (hdmi or usb) while controlling mode / zoom... ?
Definitely not with HDMI, only a few high end cameras support HDMI out in rec mode.
This camera does not appear to support standard def video out either, based on it not being mentioned in the manual, and the fact it uses micro USB (For standard def, Canon used a proprietary extension of the mini USB plug, and they don't appear to have carried this over to the micro USB cams).
That means your only option for this cam would be chdkptp live view. To use that, you'd need a USB host on board (something that runs a full linux OS, like a raspberry pi, not a microcontroller) and use the display output of that for you FPV. This is probably not a good solution, unless you already have a capable host device onboard already, and maybe not even then.
The alternative is to find a different camera that supports TV out. The specs will mention analog video out for the ones that do, and "AV Cable AVC-DC400" will be mentioned in accessories. The manual will tell you if it natively supports video out in shooting mode. If it does, the section found from "TV" in the index will mention it. If not, it will just talk about playback.
CHDK can enable analog video out in shooting mode for some cameras, but only those that physically support analog video out. See
https://chdk.setepontos.com/index.php?topic=13451.msg143315#msg143315 Only a few cameras are supported so far. It's likely that more can be added easily, but not guaranteed.
To use analog video and USB control simultaneously, you will need a custom splitter like mentioned on
https://chdk.fandom.com/wiki/USB_Remote#Note:_combined_USB_.26_Video_Connector
