I can’t connect the switch to control the light in different rooms
So, the phase goes to the lamp from the switch, and zero is usually connected directly, if the lamp with two groups of lamps, then the lamp goes one phase to each of the lamp groups from each switch button, respectively. The third core of your cable, as I understand it is not involved?
If the remaining two conductors are zero and the phase for the fixtures, then you need to apply the phase to the “middle” contact (I don’t know exactly which contact of your switch it is), take it from one of the cables, if not, take it from the nearest distribution boxes or shield), find which cable conductors go to LIGHTS and connect directly to one of the conductors to zero, to the other contact from the switch key. So do for cable and lamp in the hallway and in the kitchen.
Switch connection diagrams we examined in the articlehttps://our.electricianexp.com/en/kak-pravilno-podklyuchit-vyklyuchatel-sveta.html