[BobCratchett]

@Bob : yes no problem with icons after reboot (read my edit).

But in the end, why the problem N°1) also appear again after reboot ? Is there nothing I can do here ?

Because, for whatever reason, the widget providers aren't able to return any results when Kodi first starts. A link to a debug log (wiki) - with any debug logging option that the individual widget providers have also enabled - may provide some clues as to why, but as I said before I've only read about it once before and that with an Emby backend so it may not be an easy issue to track down.

I'm sure someone more knowledgeable than I will be alone soon.

Did you mean here instead ?

Actually I was going for the word along. I'm just a really bad typist