Can not install LINUX CNC

"W: La cible Packages (base/binary-amd64/Packages) est spécifiée plusieurs fois dans /etc/apt/sources.list.d/linuxcnc.list:1 et /etc/apt/sources.list.d/linuxcnc.list:5"

It sounds like your linuxcnc.list file has multiple repository entries for LinuxCNC.
(Probably two different versions).

You can probably correct this in the Synaptic package manager, or edit the file directly.

Which OS are you running? What is your current kernel version?

When you sorted out the apt sources, what did you end up keeping?

It might have been better to have started with the LinuxCNC Buster .iso and then swapped the kernels.

The simplest way out of this impasse is probably to install the kernel deb manually:

www.linuxcnc.org/dists/buster/base/binary-amd64/

It is possible that the problem is that there are two instances of that kernel package in the repository. I will try removing one this evening. (I can't just delete it, the index needs rebuilding and then the archive needs to be re-signed)

Download the most recent linux-image....rtai... and install it.

I typically use apt-get to install .debs, but you could also use gdebi to do it graphically, or dpkg.

The "./" before the file name is a hint to apt-get that it should look for a local file rather than on the repository.

The linux-headers package is available in the repository that you got RTAI from.

I very much suspect that there is still a problem with your apt repository settings.

If you open Synaptic and look through the menus for the repository settings, what does it have?

I think that you need a deb-src entry for www.linuxcnc.org (follow the same pattern as the others)