A way (a script ?) to automically test & heal devices?

No problem, Papy.

1 - check
2 - I see no problems there
3 - there can be a bad connection in a junction box for instance, but as you say at ‘4/’, about these issues occurring from the start, with random devices, it almost can’t be a power issue.
4 - see 3.

Oh, I just found this post about a ´brutal’ way to heal the complete mesh in one go:

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One of the possible causes I’ve read about, can be one or more ‘chatty’ devices, which can ruin (parts of) your zwave mesh.
For every device, try to set the update time of sensors as long as you find reasonable, keep away from ‘check this or that every second’ stuff.
Probably interesting topic about chatty devices: