Knowing that docker containers uses the underlying host kernel, does installing kernel module on the container (required for the process to work) affect the host kernel, or changes are relative to the container?
If it was possible to do this, it would affect the host kernel (and all other processes and containers).
By default it isn’t possible. You need to grant a container special privileges to be able to install kernel modules.
The other issue here is that Linux requires a module’s version to match exactly, so if you install a new kernel on the host, you also need to rebuild the container.