In the Kali login, I have to select
i3 in the menu in order to use i3 instead of gnome. How to set i3 as the default window manager (no need of selection?
it doesn't look like you have i3 installed from what I can see so you should:
apt-get install i3
update-alternatives --install /usr/bin/x-session-manager x-session-manager /usr/bin/i3 60
The 60 at the end sets the priority higher than the default which is 50 for gnome, so you should then auto login to i3 at that point without having to select i3, if that makes sense.