Bonjour Raphael,
For my 2 cents i would say the low compression leads to this kind of poor running and extreme mixture sensitivity. It is improving as you run it so i guess things are bedding in and compression is rising, however it sounds tight and squeaky by the end of video number 2 like it is lacking lubricant. If it were mine i would oil every moving part excessively during the bedding in period and insert a few drops of oil into the carb before each start to boost compression and lubrication. Hopefully this way will allow the process of bedding in to continue as you run it allowing internal friction to reduce and compression to rise until it runs acceptably.
Kind regards
Ade