The fact that you can't set the alarm would indicate one of the
door alarm key switches is closed when the door key cylinder
is in the straight up and down key insertion or removal position.
In this position the switch should be open.
The switch has two wires. A Light Green and a Black/White wire.
When the key lock cylinder is straight up and down (key removal
or insertion position) the switch should be open.
When you turn the key cylinder to the unlock position
the switch closes and you have continuity from the Light Green
wire to the Black/White wire. This ground signal is what disarms
the alarm. If the signal is always grounded the alarm can't be set
and is also probably what's keeping the interior lights on.
If you trace the wires down they go to a connector plug. A picture of
the harness is shown in the thread below. If you disconnect the
plug and close the doors and hatch, the interior lights should time out
and go off If either switch is the problem.
The Light Green wires from both doors are spliced together under the
dash and go to the CCM. Either switch could cause the problem.
The Black/White wire is ground.