Hi Lilian,
I connected the border router (short address 0x000), one host controlled device (short address 0x0400) and a thread router eligible end device (0x0800) to the thread network.
The interface configuration is the following :

(The border router is the second node).
- On the REED, I have the following routes :

So we can see that we are routed to the border router through the Mesh network.
From the REED and Host controlled device, all the adresses (3 devices) from "getnodesip" can ping.
2. On Windows, I had only IPv4 routes - as told before - and the interface was indeed enabled.
On the Pi (using Raspbian), the interface is enabled and has the following ipv6 addresses : fd01::84fo:whatever (global) and fe80::ff5:whatever (link)
Some routes are set, which give that the fd01:0:0:84f0:: and fe80:0:0:ff5:(full link address of the interface) go through eth1. No next hop is given.
3. Even when giving the interface -I eth1, we get either "network is unreachable" or "destination unreachable: address unreachable"
4. I have a second USB-KW41Z : the sniffer detects MLE and IEEE 802.15.4.
When REED pings eth1, it receives "Request timeout" while the sniffers identifies IEEE frames from the REED and to the REED (from Border router) containing "ACK" :

With this I feel we are really close from a result. If I get an ACK (so communication) on the MAC/PHY layer and not on the IP one, the problem should be in the configuration files (a misplaced macro) or indeed (thank you David for sharing) with a firewall or any other remaining security.
5. uname -r on the raspberry pi gives : 4.14.34-v7+
6. I've found information here - from the post you suggested - about a linux issue that would not allow Router advertisement on certain interfaces. I have indeed /proc/sys/net/ipv6/conf/eth1/accept_ra to 0, same for .../eth/autoconf and others. I will look further on that point. (Could this actually be our "firewall issue" ?)
I also noticed something that looks more like a MCUXpresso issue : the border router can be flashed by a binary file (generated by mcuxpresso) but I get an error when I launch debug directly through the IDE (still using j-link probe)
Thank you,
Sterenn